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Monte Carlo approach to the conformal bootstrap

Physical Review D 2022年第2期106卷 025019-025019页

作者： Alessandro Laio Uriel Luviano Valenzuela Marco Serone SISSA Via Bonomea 265 I-34136 Trieste Italy ICTP Strada Costiera 11 I-34151 Trieste Italy INFN Sezione di Trieste Via Valerio 2 I-34127 Trieste Italy

We introduce an approach to find approximate numerical solutions of truncated bootstrap equations for conformal field theories (CFTs) in arbitrary dimensions. The method is based on a stochastic search via a metropolis algorithm guided by an action S which is the logarithm of the truncated bootstrap equations for a single scalar field correlator. While numerical conformal bootstrap methods based on semidefinite programming put rigorous exclusion bounds on CFTs, this method looks for approximate solutions, which correspond to local minima of S, when present, and can be even far from the extremality region. By this protocol we find that if no constraint on the operator scaling dimensions is imposed, S has a single minimum, corresponding to the free theory. If we fix the external operator dimension, however, we encounter minima that can be studied with our approach. Imposing a conserved stress-tensor, a Z2 symmetry and one relevant scalar, we identify two regions where local minima of S are present. When projected in the (Δσ,Δε)-plane, σ and ε being the external and the lightest exchanged operators, one of these regions essentially coincides with the extremality line found in previous bootstrap studies. The other region is along the generalized free theories in d=2 and below that in both d=3 and d=4. We empirically prove that some of the minima found are associated to known theories, including the 2d and 3d Ising theories and the 2d Yang-Lee model.

关键词： Conformal field theory Lower-dimensional field theories metropolis algorithm Monte Carlo methods

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Generalized hydrodynamics with dephasing noise

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Physical Review B 2020年第16期102卷 161110(R)-161110(R)页

作者： Alvise Bastianello Jacopo De Nardis Andrea De Luca Institute for Theoretical Physics University of Amsterdam Science Park 904 1098 XH Amsterdam Netherlands Department of Physics and Astronomy University of Ghent Krijgslaan 281 9000 Gent Belgium Laboratoire de Physique Théorique et Modélisation (CNRS UMR 8089) Université de Cergy-Pontoise F-95302 Cergy-Pontoise France

We consider the out-of-equilibrium dynamics of an interacting integrable system in the presence of an external dephasing noise. In the limit of large spatial correlation of the noise, we develop an exact description of the dynamics of the system based on a hydrodynamic formulation. This results in an additional term to the standard generalized hydrodynamics theory describing diffusive dynamics in the momentum space of the quasiparticles of the system, with a time- and momentum-dependent diffusion constant. Our analytical predictions are then benchmarked in the classical limit by comparison with a microscopic simulation of the nonlinear Schrödinger equation, showing perfect agreement. In the quantum case, our predictions agree with state-of-the-art numerical simulations of the anisotropic Heisenberg spin in the accessible regime of times and with bosonization predictions in the limit of small dephasing times and temperatures.

关键词： Noise Nonequilibrium & irreversible thermodynamics Open quantum systems Quantum statistical mechanics Stochastic processes Lattice models in statistical physics Nonequilibrium lattice models Nonequilibrium systems Bethe ansatz Integrable systems metropolis algorithm

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Fragmented monopole crystal, dimer entropy, and Coulomb interactions in Dy2Ir2O7

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Physical Review Research 2020年第3期2卷 032073(R)-032073(R)页

作者： V. Cathelin E. Lefrançois J. Robert P. C. Guruciaga C. Paulsen D. Prabhakaran P. Lejay F. Damay J. Ollivier B. Fåk L. C. Chapon R. Ballou V. Simonet P. C. W. Holdsworth E. Lhotel Institut Néel CNRS & Université Grenoble Alpes F-38042 Grenoble France Institut Laue Langevin CS 20156 F-38042 Grenoble France Centro Atómico Bariloche Comisión Nacional de Energía Atómica (CNEA) Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) Avenida E. Bustillo 9500 R8402AGP San Carlos de Bariloche Río Negro Argentina Clarendon Laboratory Physics Department Oxford University Oxford OX1 3PU United Kingdom Laboratoire Léon Brillouin Université Paris-Saclay CNRS CEA CEA-Saclay F-91191 Gif-sur-Yvette France Diamond Light Source Limited Harwell Science and Innovation Campus Didcot United Kingdom Université de Lyon ENS de Lyon Université Claude Bernard CNRS Laboratoire de Physique F-69342 Lyon France

Neutron scattering, specific-heat, and magnetization measurements on both powders and single crystals reveal that Dy2Ir2O7 realizes the fragmented monopole crystal state in which antiferromagnetic order and a Coulomb phase spin liquid coinhabit. The measured residual entropy is that of a hard-core dimer liquid, as predicted. Inclusion of Coulomb interactions allows for a quantitative description of both the thermodynamic data and the magnetization dynamics, with the energy scale given by deconfined defects in the emergent ionic crystal. Our data reveal low-energy excitations, as well as a large distribution of energy barriers down to low temperatures, while the magnetic response to an applied field suggests that domain wall pinning is important, results that call for further theoretical modeling.

关键词： Exotic phases of matter Frustrated magnetism Magnetic interactions Magnetism Quasiparticles & collective excitations Spin dynamics Spin ice AC susceptibility measurements Dilution refrigerator Magnetization measurements metropolis algorithm Neutron diffraction Specific heat measurements Spin lattice models

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A Bayesian zero-inflated binomial regression and its application in dose-finding study

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JOURNAL OF BIOPHARMACEUTICAL STATISTICS 2020年第2期30卷 322-333页

作者： Wanitjirattikal, Puntipa Shi, Chenyang King Mongkuts Inst Technol Ladkrabang Dept Stat Bangkok Thailand Celgene Corp Dept Biostat Berkeley Hts NJ 07922 USA

In early phase clinical trial, finding maximum-tolerated dose (MTD) is a very important goal. Many researches show that finding a correct MTD can improve drug efficacy and safety significantly. Usually, dose-finding trials start from very low doses, so in many cases, more than 50% patients or cohorts do not have dose-limiting toxicity (DLT), but DLT may occur suddenly and increase fast along with just two or three doses. Although some fantastic models were built to find MTD, little consideration was given to those '0 DLTs' and the 'jump' of DLTs. In this paper, we developed a Bayesian zero-inflated binomial regression for dose-finding study, which analyses dose-finding data from two aspects: 1) observation of only zeros, 2) number of DLTs based on binomial distribution, so it can help us analyse if the cohorts without DLT have potential possibility to have DLT and fit the 'jump' of DLTs.

关键词： Dose-limiting toxicity maximum-tolerated dose metropolis algorithm zero-inflated binomial regression

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Wind field reconstruction with adaptive random Fourier features

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PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 2021年第2255期477卷 20210236-20210236页

作者： Kiessling, Jonas Strom, Emanuel Tempone, Raul H Ai AB Stockholm Sweden KTH Royal Inst Technol Stockholm Sweden Rhein Westfal TH Aachen Aachen Germany KAUST Thuwal Saudi Arabia

We investigate the use of spatial interpolation methods for reconstructing the horizontal near-surface wind field given a sparse set of measurements. In particular, random Fourier features is compared with a set of benchmark methods including kriging and inverse distance weighting. Random Fourier features is a linear model beta(x)= Sigma(K)(k-1) beta(k) e(i omega kx) approximating the velocity field, with randomly sampled frequencies omega(k) and amplitudes beta(k) trained to minimize a loss function. We include a physically motivated divergence penalty vertical bar del. beta(x)vertical bar(2), as well as a penalty on the Sobolev norm of beta. We derive a bound on the generalization error and a sampling density that minimizes the bound. We then devise an adaptive metropolis-Hastings algorithm for sampling the frequencies of the optimal distribution. In our experiments, our random Fourier features model outperforms the benchmark models.

关键词： random Fourier features metropolis algorithm spatial interpolation machine learning wind field reconstruction flow field estimation

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Classical statistical mechanics in the grand canonical ensemble

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Physical Review E 2021年第1期104卷 014117-014117页

作者： Philipp Ströker Karsten Meier Institut für Thermodynamik Helmut-Schmidt-Universität/Universität der Bundeswehr Hamburg Holstenhofweg 85 22043 Hamburg Germany

The methodology developed by Lustig for calculating thermodynamic properties in the microcanonical and canonical ensembles [J. Chem. Phys. 100, 3048 (1994); Mol. Phys. 110, 3041 (2012)] is applied to derive rigorous expressions for thermodynamic properties of fluids in the grand canonical ensemble. All properties are expressed by phase-space functions, which are related to derivatives of the grand canonical potential with respect to the three independent variables of the ensemble: temperature, volume, and chemical potential. The phase-space functions contain ensemble averages of combinations of the number of particles, potential energy, and derivatives of the potential energy with respect to volume. In addition, expressions for the phase-space functions for temperature-dependent potentials are provided, which are required to account for quantum corrections semiclassically in classical simulations. Using the Lennard-Jones model fluid as a test case, the derived expressions are validated by Monte Carlo simulations. In contrast to expressions for the thermal expansion coefficient, the isothermal compressibility, and the thermal pressure coefficient from the literature, our expressions yield more reliable results for these properties, which agree well with a recent accurate equation of state for the Lennard-Jones model fluid. Moreover, they become equivalent to the corresponding expressions in the canonical ensemble in the thermodynamic limit.

关键词： Classical statistical mechanics Equations of state metropolis algorithm Monte Carlo methods

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Recognition capabilities of a Hopfield model with auxiliary hidden neurons

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Physical Review E 2021年第6期103卷 L060401-L060401页

作者： Marco Benedetti Victor Dotsenko Giulia Fischetti Enzo Marinari Gleb Oshanin Università di Roma La Sapienza Piazzale Aldo Moro 5 I-00185 Rome Italy Sorbonne Université CNRS Laboratoire de Physique Théorique de la Matière Condensée (UMR 7600) 4 Place Jussieu F-75252 Paris Cedex 05 France CNR-Nanotec and INFN Sezione di Roma 1 I-00185 Rome Italy

We study the recognition capabilities of the Hopfield model with auxiliary hidden layers, which emerge naturally upon a Hubbard-Stratonovich transformation. We show that the recognition capabilities of such a model at zero temperature outperform those of the original Hopfield model, due to a substantial increase of the storage capacity and the lack of a naturally defined basin of attraction. The modified model does not fall abruptly into the regime of complete confusion when memory load exceeds a sharp threshold. This latter circumstance, together with an increase of the storage capacity, renders such a modified Hopfield model a promising candidate for further research, with possible diverse applications.

关键词： Critical phenomena Memory Order parameters Phase diagrams Transition temperature Disordered systems Spin glasses Hopfield model metropolis algorithm Monte Carlo methods

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Overscreening and Underscreening in Solid-Electrolyte Grain Boundary Space-Charge Layers

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Physical Review Letters 2021年第13期127卷 135502-135502页

作者： Jacob M. Dean Samuel W. Coles William R. Saunders Andrew R. McCluskey Matthew J. Wolf Alison B. Walker Benjamin J. Morgan Department of Chemistry University of Bath Claverton Down BA2 7AY United Kingdom The Faraday Institution Quad One Harwell Science and Innovation Campus Didcot OX11 0RA United Kingdom Department of Physics University of Bath Claverton Down BA2 7AY United Kingdom European Spallation Source ERIC P.O. Box 176 SE-221 00 Lund Sweden

Polycrystalline solids can exhibit material properties that differ significantly from those of equivalent single-crystal samples, in part, because of a spontaneous redistribution of mobile point defects into so-called space-charge regions adjacent to grain boundaries. The general analytical form of these space-charge regions is known only in the dilute limit, where defect-defect correlations can be neglected. Using kinetic Monte Carlo simulations of a three-dimensional Coulomb lattice gas, we show that grain boundary space-charge regions in nondilute solid electrolytes exhibit overscreening—damped oscillatory space-charge profiles—and underscreening—decay lengths that are longer than the corresponding Debye length and that increase with increasing defect-defect interaction strength. Overscreening and underscreening are known phenomena in concentrated liquid electrolytes, and the observation of functionally analogous behavior in solid electrolyte space-charge regions suggests that the same underlying physics drives behavior in both classes of systems. We therefore expect theoretical approaches developed to study nondilute liquid electrolytes to be equally applicable to future studies of solid electrolytes.

关键词： Solid-state chemistry Ionic solids Solid-solid interfaces Lattice models in condensed matter metropolis algorithm

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Low-temperature ordering of the dimer phase of a two-dimensional model of core-softened particles

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Physical Review E 2021年第4期104卷 044602-044602页

作者： F. Mambretti M. Martinelli F. Civillini M. Bertoletti S. Riva N. Manini D. E. Galli D. Pini Università degli Studi di Milano Dipartimento di Fisica “Aldo Pontremoli” via Celoria 16 20133 Milan Italy Università degli Studi di Padova Dipartimento di Fisica e Astronomia via Marzolo 8 35131 Padua Italy

Purely pairwise interactions of the core-softened type, i.e., featuring a soft repulsion followed by a hard-core interaction at shorter distance, give rise to nontrivial equilibrium structures entirely different from the standard close packing of spheres. In particular, in a suitable low-temperature region of their phase diagram, such interactions are well known to favor a transition from a fluid to a cluster crystal. The residual mutual interaction between individual clusters can lead to the formation of patterns of their reciprocal orientations. In this work, we investigate two examples of such models in two dimensions, at the density most appropriate to the dimer phase, whereby clusters consist of just two particles, studying them with optimization techniques and Monte Carlo simulations. We focus on the dimer crystal, and unveil a second phase transition at extremely low temperature. This transition leads from a triangular dimer lattice with randomly disordered dimer orientations at high temperature to a reduced-symmetry ground state with nematic orientational order and a slightly distorted structure characterized by a centered-rectangular lattice at low temperature.

关键词： Crystal defects Distortions & defects Nematic order Quasicrystalline structure 2-dimensional systems Soft colloids Density functional theory metropolis algorithm Monte Carlo methods

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Melting in two-dimensional systems: Characterizing continuous and first-order transitions

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Physical Review B 2021年第9期103卷 094107-094107页

作者： Óscar Toledano M. Pancorbo J. E. Alvarellos Óscar Gálvez Departamento Física Interdisciplinar Facultad de Ciencias Universidad Nacional de Educación a Distancia (UNED) Senda del Rey 9 28040 Madrid Spain Departamento Física Fundamental Facultad de Ciencias Universidad Nacional de Educación a Distancia (UNED) Senda del Rey 9 28040 Madrid Spain

The mechanisms underlying the melting process in bidimensional systems have been widely studied by means of experiments, theory, and simulations since Kosterlitz, Thouless, Halperin, Nelson, and Young elaborated the KTHNY theory. In the framework of this theory, melting is produced by two continuous transitions mediated by the unbinding of local defects and the appearance of an intermediate phase between solid and liquid, called “hexatic.” There are also other competing theories that could explain this process, as, e.g., the formation of grain boundaries (lines of defects), which lead to a first-order transition. In this paper, simulations of systems interacting via the Lennard Jones 6–12 and Morse potentials using the metropolis Monte Carlo method in the NVT ensemble have been performed to study the effect of the potential shape in the melting process. Additionally, truncated Morse potentials (with only a repulsive part) have been used to investigate the effect of the long-range interactions. Transitions from solid to hexatic phases were found to be continuous for all potentials studied, but transitions from hexatic to liquid phases were found to be either continuous or first order, depending on the thermodynamic conditions and the potential interaction selected, suggesting that melting can be triggered by different mechanisms, like grain boundary formation or defect unbinding. We find that the ratio of defects at the liquid-hexatic or liquid-coexistence phase transitions could determine the nature of these transitions and the mechanism underlying the melting process. The effect of the interaction of particles with their first- and second-nearest neighbors is also discussed.

关键词： Dynamical phase transitions First order phase transitions Geometric & topological phases Second order phase transitions Topological phase transition 2-dimensional systems Ultrathin films metropolis algorithm

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