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First-order phase transitions in Yang-Mills theories and the density of state method

Physical Review D 2023年第7期108卷 074517-074517页

作者： Biagio Lucini David Mason Maurizio Piai Enrico Rinaldi Davide Vadacchino Department of Mathematics Faculty of Science and Engineering Swansea University Fabian Way Swansea SA1 8EN Wales United Kingdom and Swansea Academy of Advanced Computing Swansea University Fabian Way Swansea SA1 8EN Wales United Kingdom Department of Physics Faculty of Science and Engineering Swansea University Singleton Park Swansea SA2 8PP Wales United Kingdom and Department of Mathematics Faculty of Science and Engineering Swansea University Fabian Way Swansea SA1 8EN Wales United Kingdom Department of Physics Faculty of Science and Engineering Swansea University Singleton Park Swansea SA2 8PP Wales United Kingdom Interdisciplinary Theoretical and Mathematical Science Program RIKEN (iTHEMS) 2-1 Hirosawa Wako Saitama 351-0198 Japan School of Mathematics and Hamilton Mathematics Institute Trinity College Dublin 2 Ireland and Centre for Mathematical Sciences University of Plymouth Plymouth PL4 8AA United Kingdom

When studied at finite temperature, Yang-Mills theories in 3+1 dimensions display the presence of confinement/deconfinement phase transitions, which are known to be of first order—the SU(2) gauge theory being the exception. Theoretical as well as phenomenological considerations indicate that it is essential to establish a precise characterization of these physical systems in proximity of such phase transitions. We present and test a new method to study the critical region of parameter space in non-Abelian quantum field theories on the lattice, based upon the logarithmic linear relaxation (LLR) algorithm. We apply this method to the SU(3) Yang-Mills lattice gauge theory, and perform extensive calculations with one fixed choice of lattice size. We identify the critical temperature, and measure interesting physical quantities near the transition. Among them, we determine the free energy of the model in the critical region, exposing for the first time its multivalued nature with a numerical calculation from first principles, providing this novel evidence in support of a first-order phase transition. This study sets the stage for future high-precision measurements, by demonstrating the potential of the method.

关键词： Color confinement Confinement First order phase transitions Lattice field theory Lattice gauge theory heatbath algorithm Numerical approximation & analysis

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Fluctuation relations in a nonequilibrium system: Surface tension and effective temperature in an Ising-doped voter model

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Physical Review E 2022年第6期105卷 064120-064120页

作者： Jerzy Batygolski Aleksandra Napierała-Batygolska Adam Lipowski Faculty of Physics Adam Mickiewicz University Poznań Poland

Fluctuation relations of Jarzynski and Crooks enable efficient calculations of a free-energy difference between equilibrium states. In the present paper, we provide some numerical evidence that these relations can also be used for a two-dimensional Ising-doped voter model, which is a nonequilibrium system with a violated detailed balance. Adopting the method of Híjar and Sutmann, we implement a protocol that switches between periodic and antiperiodic boundary conditions and induces formation of an interface in the model. Assuming that a suitably interpreted Ising Hamiltonian can be considered as a pseudoenergy of the model, we examine fluctuations of work performed during these processes and estimate the surface tension. Our results confirm that the surface tension remains positive in this model except a limiting case of the voter model, where it seems to vanish. Comparing the free-energy estimates at different speeds of the switching process, we also estimate an effective temperature in the model. Perhaps coincidentally, the effective temperature of the voter model appears to be close to the critical temperature of the Ising model.

关键词： Classical statistical mechanics Fluctuation theorems Nonequilibrium statistical mechanics Classical spin models Equilibrium lattice models Lattice models in statistical physics Nonequilibrium lattice models heatbath algorithm Ising model Monte Carlo methods

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Strings of diquark-quark (QQ)Q baryon before the phase transition

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Physical Review D 2023年第9期108卷 094502-094502页

作者： A. S. Bakry M. A. Deliyergiyev A. A. Galal M. N. Khalil Department of Mathematics Bergische Universität Wuppertal 42097 Germany Department of Physics University of Ferrara Ferrara 44121 Italy Computation-based science Research center Cyprus Institute Nicosia 2121 Cyprus

We explore the limit at which the effective baryonic Y-string model of the junction approaches the mesonic stringlike behavior. We calculate and compare the numerical values of the static potential and energy-density correlators of diquark-quark and quark-antiquark configurations. The gauge model is pure Yang-Mills SU(3) lattice gauge theory at coupling β=6.0 and finite temperature. The diquark setup is approximated as two quarks confined within a sphere of radius 0.1 fm. The lattice data of the potential and energy show that the string binding the diquark-quark configuration displays an identical behavior to the quark-antiquark confining string. However, with the temperature increase to a small enough neighborhood of the critical point Tc, the gluonic similarities between the two systems do not manifest neither at short nor intermediate distance scales R<1.0 fm. The comparison between the potential and the second moment of the action-density correlators for both systems shows significant splitting. This suggests that subsisted baryonic decoupled states overlap with the mesonic spectrum. The baryonic junction’s model for the potential and the profile returns a good fit to the numerical lattice data of the diquark-quark arrangement. However, near the critical point, the mesonic string displays large deviations compared to fits of the corresponding quark-antiquark data.

关键词： Color confinement Field & string theory models & techniques Finite temperature field theory Geometry Higher-dimensional field theories Lattice QCD Lattice field theory Multiquark bound states Phenomenology Quark model String phenomenology Strings & branes Topology Baryons Hadrons Mesons heatbath algorithm Lattice gauge theory Metropolis algorithm Particle interactions Path-integral Monte Carlo

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U(N) gauge theory in the strong coupling limit on a quantum annealer

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Physical Review D 2023年第7期108卷 074501-074501页

作者： Jangho Kim Thomas Luu Wolfgang Unger Institute for Advanced Simulation (IAS-4) Forschungszentrum Jülich 54245 Jülich Germany Institut für Kernphysik (IKP-3) Forschungszentrum Jülich 54245 Jülich Germany Fakultät für Physik Bielefeld University D-33615 Bielefeld Germany

Lattice QCD in the strong coupling regime can be formulated in dual variables, which are integer-valued. It can be efficiently simulated for modest finite temperatures and finite densities via the worm algorithm, circumventing the finite density sign problem in this regime. However, the low temperature regime is more expensive to address. As the partition function is solely expressed in terms of integers, it can be cast as a combinatorial optimization problem that can be solved on a quantum annealer. We will first explain the setup of the system we want to study and then present its reformulation suitable for a quantum annealer, and in particular the D wave. As a proof of concept, we present first results obtained on D wave for gauge group U(1) and U(3), and outline the next steps towards gauge groups SU(3). We find that in addition, histogram reweighting greatly improves the accuracy of our observables when compared to analytic results.

关键词： Effective field theory Lattice QCD QCD phase transitions Quantum computation heatbath algorithm Monte Carlo methods Quantum Monte Carlo

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Lattice protein design using Bayesian learning

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Physical Review E 2021年第1期104卷 014404-014404页

作者： Tomoei Takahashi George Chikenji Kei Tokita Graduate School of Informatics Nagoya University Nagoya 464-8601 Japan Graduate School of Engineering Nagoya University Nagoya 464-8603 Japan

Protein design is the inverse approach of the three-dimensional (3D) structure prediction for elucidating the relationship between the 3D structures and amino acid sequences. In general, the computation of the protein design involves a double loop: A loop for amino acid sequence changes and a loop for an exhaustive conformational search for each amino acid sequence. Herein, we propose a novel statistical mechanical design method using Bayesian learning, which can design lattice proteins without the exhaustive conformational search. We consider a thermodynamic hypothesis of the evolution of proteins and apply it to the prior distribution of amino acid sequences. Furthermore, we take the water effect into account in view of the grand canonical picture. As a result, on applying the 2D lattice hydrophobic-polar (HP) model, our design method successfully finds an amino acid sequence for which the target conformation has a unique ground state. However, the performance was not as good for the 3D lattice HP models compared to the 2D models. The performance of the 3D model improves on using a 20-letter lattice proteins. Furthermore, we find a strong linearity between the chemical potential of water and the number of surface residues, thereby revealing the relationship between protein structure and the effect of water molecules. The advantage of our method is that it greatly reduces computation time, because it does not require long calculations for the partition function corresponding to an exhaustive conformational search. As our method uses a general form of Bayesian learning and statistical mechanics and is not limited to lattice proteins, the results presented here elucidate some heuristics used successfully in previous protein design methods.

关键词： heatbath algorithm

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Time evolution with symmetric stochastic action

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Physical Review Research 2021年第1期3卷 013240-013240页

作者： Peter D. Drummond Centre for Quantum and Optical Science Swinburne University of Technology Melbourne 3122 Australia Institute of Theoretical Atomic Molecular and Optical Physics (ITAMP) Harvard University Cambridge 02138 MA United States Weizmann Institute of Science Rehovot 7610001 Israel

The time evolution of quantum fields is shown to be equivalent to a time-symmetric Fokker-Planck equation. Results are obtained using a Q-function representation, including fermion-fermion, boson-boson, and fermion-boson interactions with linear, quadratic, cubic, and quartic Hamiltonians, typical of QED and many other cases. For local boson-boson coupling, the resulting probability distribution is proved to have a positive, time-symmetric path integral and action principle, leading to a forward-backward stochastic process in both time directions. The solution corresponds to a c-number field equilibrating in an additional dimension. Paths are stochastic trajectories of fields in space-time, which are samples of a statistical mechanical steady state in a higher-dimensional space. We derive numerical methods and examples of solutions to the resulting stochastic partial differential equations in a higher time dimension, giving agreement with examples of simple bosonic quantum dynamics. This approach may lead to useful computational techniques for quantum field theory, as well as to new ontological models of physical reality.

关键词： Bose-Einstein condensates Path integrals Quantum field theory heatbath algorithm Quantum Monte Carlo Quantum theory

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Speed Inversion in a Potts Glass Model of Cortical Dynamics

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PRX Life 2023年第1期1卷 013005-013005页

作者： Kwang Il Ryom Alessandro Treves

To better understand the conditions prevailing when acquiring complex, compositional memories, we introduce, in a previously studied Potts model of long-range cortical interactions, a differentiation between a frontal and a posterior subnetwork. “Frontal” units, representing patches of anterior cortex, are endowed with a higher number S of local attractor states, in keeping with the larger number of local synaptic contacts of neurons there, than in some posterior, e.g., occipital, cortices. A thermodynamic analysis and computer simulations confirm that disorder leads to glassy properties and slow dynamics but, surprisingly, the frontal network, which would be slower if isolated, becomes faster than the posterior network when interacting with it. From an abstract, drastically simplified model we take some steps towards approaching a neurally plausible one, and find that the speed inversion effect is basically preserved. We argue that this effect may facilitate learning, through the acquisition of new dynamical attractors.

关键词： Complex systems Memory Neuroscience Cortical networks Spin glasses Collective dynamics heatbath algorithm Replica theory

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Magnetic ordering of random dense packings of freely rotating dipoles

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Physical Review B 2020年第18期102卷 184423-184423页

作者： Juan J. Alonso B. Allés V. Russier Física Aplicada I Universidad de Málaga 29071 Málaga Spain Instituto Carlos I de Física Teórica y Computacional Universidad de Málaga 29071 Málaga Spain INFN–Sezione di Pisa Largo Pontecorvo 3 56127 Pisa Italy ICMPE UMR 7182 CNRS and UPE 2-8 rue Henri Dunant 94320 Thiais France

We study random dense packings of Heisenberg dipoles by numerical simulation. The dipoles are at the centers of identical spheres that occupy fixed random positions in space and fill a fraction Φ of the spatial volume. The parameter Φ ranges from rather low values, typical of amorphous ensembles, to the maximum Φ=0.64 that occurs in the random-close-packed limit. We assume that the dipoles can freely rotate and have no local anisotropies. As well as the usual thermodynamical variables, the physics of such systems depends on Φ. Concretely, we explore the magnetic ordering of these systems in order to depict the phase diagram in the temperature-Φ plane. For Φ≳0.49 we find quasi-long-range ferromagnetic order coexisting with strong long-range spin-glass order. For Φ≲0.49 the ferromagnetic order disappears giving way to a spin-glass phase similar to the ones found for Ising dipolar systems with strong frozen disorder.

关键词： Dipolar interaction Frustrated magnetism Magnetic phase transitions Phase diagrams Classical spin models Magnetic nanoparticles Spin glasses heatbath algorithm

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Nonequilibrium phase transition in an Ising model without detailed balance

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Physical Review E 2020年第5期102卷 052111-052111页

作者： Manoj Kumar Chandan Dasgupta Centre for Fluid and Complex Systems Coventry University Coventry CV1 5FB United Kingdom International Centre for Theoretical Sciences Tata Institute of Fundamental Research Bengaluru 560089 India Department of Physics Indian Institute of Science Bengaluru 560012 India

We study a two-dimensional ferromagnetic Ising model in which spins are updated using modified versions of the Metropolis and Glauber algorithms. These update rules do not obey the detailed balance condition. The steady-state behavior of the model is studied using molecular field theory and Monte Carlo simulations. This model is found to exhibit a nonequilibrium phase transition from a “paramagnetic” state with zero magnetization to a “ferromagnetic” state with nonzero magnetization as the variable that plays the role of temperature in the spin updates is decreased. From detailed Monte Carlo simulations using the modified Metropolis algorithm, we demonstrate explicitly the nonequilibrium nature of the transition and show that it cannot be described as an equilibrium transition with an effective temperature different from the temperature used in the spin updates. The critical exponents that characterize the singular behavior near this continuous phase transition are calculated from finite size scaling of specific heat, magnetization, susceptibility, and correlation length. We find that the values of these exponents are the same (within error bars) as those of the equilibrium Ising model in two dimensions.

关键词： Classical statistical mechanics Critical exponents Critical phenomena Phase transitions Finite-size scaling heatbath algorithm Ising model Mean field theory Metropolis algorithm

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Analysis of dynamic Ising model by a variational approximate method: Estimation of transfer entropy

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Physical Review E 2020年第4期101卷 042102-042102页

作者： Hirohito Kiwata Division of Natural Science Osaka Kyoiku University Kashiwara Osaka 582-8582 Japan

Transfer entropy is an important index for investigating the causal relationship between random variables. It is known that a phase transition can be detected by transfer entropy. In this work, I propose a method for obtaining the transfer entropy by applying the variational approximation method to a dynamic Ising model. Our method is also effective for dynamics that do not satisfy the detailed balance condition. Our method finds the transfer entropy by solving a transcendental equation. When compared with the transfer entropy obtained by Monte Carlo sampling, it was found that they qualitatively matched near the transition point; moreover, the match was obtained with good accuracy in the region deviated from the transition point.

关键词： Stochastic processes Stochastic dynamical systems heatbath algorithm Information theory Markovian processes Mean-field & cluster methods Stochastic analysis Stochastic analysis methods Time series analysis

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