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Lattice QCD constraints on the heavy quark diffusion coefficient

Physical Review D 2020年第7期102卷 074503-074503页

作者： Nora Brambilla Viljami Leino Peter Petreczky Antonio Vairo Physik Department Technische Universität München James-Franck-Strasse 1 85748 Garching Germany Institute for Advanced Study Technische Universität München Lichtenbergstrasse 2a 85748 Garching Germany Physics Department Brookhaven National Laboratory Upton New York 11973 USA

We report progress toward computing the heavy quark momentum diffusion coefficient from the correlator of two chromoelectric fields attached to a Polyakov loop in pure SU(3) gauge theory. Using a multilevel algorithm and tree-level improvement, we study the behavior of the diffusion coefficient as a function of temperature in the wide range 1.1

关键词： Lattice field theory Quantum chromodynamics Quark-gluon plasma Strong interaction heatbath algorithm Lattice gauge theory

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Acceptance rate is a thermodynamic function in local Monte Carlo algorithms

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Physical Review E 2019年第6期100卷 063303-063303页

作者： Evgeni Burovski Wolfhard Janke Maria Guskova Lev Shchur National Research University Higher School of Economics 101000 Moscow Russia Institut für Theoretische Physik Universität Leipzig IPF 231101 04081 Leipzig Germany Landau Institute for Theoretical Physics 142432 Chernogolovka Russia

We study properties of Markov chain Monte Carlo simulations of classical spin models with local updates. We derive analytic expressions for the mean value of the acceptance rate of single-spin-flip algorithms for the one-dimensional Ising model. We find that for the Metropolis algorithm the average acceptance rate is a linear function of energy. We further provide numerical results for the energy dependence of the average acceptance rate for the three- and four-state Potts model, and the XY model in one and two spatial dimensions. In all cases, the acceptance rate is an almost linear function of the energy in the critical region. The variance of the acceptance rate is studied as a function of the specific heat. While the specific heat develops a singularity in the vicinity of a phase transition, the variance of the acceptance rate stays finite.

关键词： Classical statistical mechanics Classical spin models heatbath algorithm Metropolis algorithm Monte Carlo methods

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Emergence of long-range magnetic order stabilized by magnetic impurities in pnictides

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Physical Review B 2019年第21期99卷 214439-214439页

作者： Carla Lupo Thomas Julian Roberts Cedric Weber Theory and Simulation of Condensed Matter The Strand King's College London WC2R 2LS London United Kingdom

The Mermin-Wagner theorem prevents the stabilization of long-range magnetic order in two-dimensional layered materials, such as the pnictide superconductors, unless the magnetism is associated with a discrete symmetry breaking. A typical known example is the discrete row and column collinear magnetic state that emerges in doped iron pnictide materials due to an order-by-disorder mechanism. In these compounds, the magnetic state competes with superconductivity and the mechanism that stabilizes magnetism remains controversial. In this work, we report the phase diagram of a doped frustrated Heisenberg model obtained through Monte Carlo simulations combined with a parallel tempering simulation technique. The emergence of long-range magnetic order is stabilized by interactions between the magnetic dopant impurities.

关键词： First order phase transitions Impurities in superconductors Magnetic interactions Nematic order Percolation Second order phase transitions Stripes Vacancies Lattice models in statistical physics Pnictides heatbath algorithm Heisenberg model Monte Carlo methods O(N) symmetry Z_2 symmetry

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Six-vertex model and Schramm-Loewner evolution

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Physical Review E 2017年第5期95卷 052146-052146页

作者： Richard Kenyon Jason Miller Scott Sheffield David B. Wilson Department of Mathematics Brown University 1 Prospect Street Providence Rhode Island 02912 USA Statistical Laboratory Centre for Mathematical Sciences University of Cambridge Wilberforce Road Cambridge CB3 0WB United Kingdom Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge Massachusetts 02139 USA Microsoft Research One Microsoft Way Redmond Washington 98052 USA

Square ice is a statistical mechanics model for two-dimensional ice, widely believed to have a conformally invariant scaling limit. We associate a Peano (space-filling) curve to a square ice configuration, and more generally to a so-called six-vertex model configuration, and argue that its scaling limit is a space-filling version of the random fractal curve SLEκ, Schramm-Loewner evolution with parameter κ, where 4<κ≤12+82. For square ice, κ=12. At the “free-fermion point” of the six-vertex model, κ=8+43. These unusual values lie outside the classical interval 2≤κ≤8.

关键词： Critical phenomena Equilibrium lattice models Combinatorics Conformal field theory Finite-size scaling Fractal dimension characterization heatbath algorithm

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Domain state of the axial next-nearest-neighbor Ising model in two dimensions

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Physical Review B 2017年第17期95卷 174409-174409页

作者： Fumitaka Matsubara Takayuki Shirakura Nobuo Suzuki Faculty of Science and Technology Tohoku Bunka Gakuen University Sendai 980-8551 Japan

We have examined the spin ordering of an axial next-nearest-neighbor Ising model in two dimensions (2D) near above the antiphase (〈2〉 phase). We considered an NR-replica system and calculated an overlap function qm between different replicas, having used a cluster heat bath Monte Carlo method. We determined transition temperature between the 〈2〉 phase and a floating incommensurate (IC) phase as TC2/J=0.89±0.01 with frustration ratio κ(≡−J2/J1)=0.6. We found that the spin state at T≳TC2 may be called a domain state, because the spin structure is characterized by a sequentially arranged four types of domains with different 〈2〉 structures. In the domain state, the 2D XY symmetry of the spin correlation in the IC phase weakly breaks, and the diversity of the spin arrangement increases as T→TC2. The Binder ratio gL exhibits a depression at T∼TC2 and the quasiperiodic spin structure, which is realized in the IC phase, becomes diverse at T≳TC2. We discussed that the domain state is stable against the thermal fluctuation which brings a two-stage development of the spin structure at low temperatures.

关键词： Magnetic phase transitions heatbath algorithm Monte Carlo methods

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Machine learning of explicit order parameters: From the Ising model to SU(2) lattice gauge theory

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Physical Review B 2017年第18期96卷 184410-184410页

作者： Sebastian J. Wetzel Manuel Scherzer Institut für Theoretische Physik Universität Heidelberg Philosophenweg 16 69120 Heidelberg Germany

We present a solution to the problem of interpreting neural networks classifying phases of matter. We devise a procedure for reconstructing the decision function of an artificial neural network as a simple function of the input, provided the decision function is sufficiently symmetric. In this case one can easily deduce the quantity by which the neural network classifies the input. The method is applied to the Ising model and SU(2) lattice gauge theory. In both systems we deduce the explicit expressions of the order parameters from the decision functions of the neural networks. We assume no prior knowledge about the Hamiltonian or the order parameters except Monte Carlo–sampled configurations.

关键词： Classical statistical mechanics Gauge theories Machine learning Order parameters Phase transitions heatbath algorithm Ising model Lattice gauge theory Metropolis algorithm Monte Carlo methods Simulated annealing

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Honeycomb-Lattice Heisenberg-Kitaev Model in a Magnetic Field: Spin Canting, Metamagnetism, and Vortex Crystals

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Physical Review Letters 2016年第27期117卷 277202-277202页

作者： Lukas Janssen Eric C. Andrade Matthias Vojta Institut für Theoretische Physik Technische Universität Dresden 01062 Dresden Germany Instituto de Física de São Carlos Universidade de São Paulo C.P. 369 São Carlos São Paulo 13560-970 Brazil

The Heisenberg-Kitaev model is a paradigmatic model to describe the magnetism in honeycomb-lattice Mott insulators with strong spin-orbit coupling, such as A2IrO3 (A=Na, Li) and α−RuCl3. Here, we study in detail the physics of the Heisenberg-Kitaev model in an external magnetic field. Using a combination of Monte Carlo simulations and spin-wave theory, we map out the classical phase diagram for different directions of the magnetic field. Broken SU(2) spin symmetry renders the magnetization process rather complex, with sequences of phases and metamagnetic transitions. In particular, we find various large-unit-cell and multi-Q phases including a vortex-crystal phase for a field in the [111] direction. We also discuss quantum corrections in the high-field phase.

关键词： Frustrated magnetism Magnetic phase transitions Honeycomb lattice Mott insulators heatbath algorithm Holstein-Primakoff method Kitaev-Heisenberg model

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Metastable minima of the Heisenberg spin glass in a random magnetic field

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Physical Review E 2016年第5期94卷 052143-052143页

作者： Auditya Sharma Joonhyun Yeo M. A. Moore Department of Physics Indian Institute of Science Education and Research Bhopal India Department of Physics Konkuk University Seoul 143-701 Korea School of Physics and Astronomy University of Manchester Manchester M13 9PL United Kingdom

We have studied zero-temperature metastable minima in classical m-vector component spin glasses in the presence of m-component random fields for two models, the Sherrington-Kirkpatrick (SK) model and the Viana-Bray (VB) model. For the SK model we have calculated analytically its complexity (the log of the number of minima) for both the annealed case where one averages the number of minima before taking the log and the quenched case where one averages the complexity itself, both for fields above and below the de Almeida-Thouless (AT) field, which is finite for m>2. We have done numerical quenches starting from a random initial state (infinite temperature state) by putting spins parallel to their local fields until there is no further decrease of the energy and found that in zero field it always produces minima that have zero overlap with each other. For the m=2 and m=3 cases in the SK model the final energy reached in the quench is very close to the energy Ec at which the overlap of the states would acquire replica symmetry-breaking features. These minima have marginal stability and will have long-range correlations between them. In the SK limit we have analytically studied the density of states ρ(λ) of the Hessian matrix in the annealed approximation. Despite the fact that in the presence of a random field there are no continuous symmetries, the spectrum extends down to zero with the usual λ form for the density of states for fields below the AT field. However, when the random field is larger than the AT field, there is a gap in the spectrum, which closes up as the AT field is approached. The VB model behaves differently and seems rather similar to studies of the three-dimensional Heisenberg spin glass in a random vector field.

关键词： Specific phase transitions Spin glasses Finite-size scaling heatbath algorithm Replica methods Replica theory XYZ model

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Gibbs sampling of complex-valued distributions

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Physical Review D 2016年第7期94卷 074503-074503页

作者： L. L. Salcedo Departamento de Física Atómica Molecular y Nuclear and Instituto Carlos I de Física Teórica y Computacional Universidad de Granada E-18071 Granada Spain

A new technique is explored for the Monte Carlo sampling of complex-valued distributions. The method is based on a heat bath approach where the conditional probability is replaced by a positive representation of it on the complex plane. Efficient ways to construct such representations are also introduced. The performance of the algorithm is tested on small and large lattices with a λϕ4 theory with quadratic nearest-neighbor complex coupling. The method works for moderate complex couplings, reproducing reweighting and complex Langevin results and fulfilling various Schwinger-Dyson relations.

关键词： Lattice field theory heatbath algorithm Monte Carlo methods

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