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Effect of next nearest neighbour interactions on compensation temperature in trilayered spin systems

PHASE TRANSITIONS 2022年第8-9期95卷 642-650页

作者： Guru, Enakshi Saha, Sonali Sarojini Naidu Coll Women Dept Phys Kolkata India

In this paper we are communicating a Monte-Carlo based numerical study on the ABA type trilayered Ising spin system incorporating next nearest neighbour interactions. The ABA type system is of growing interest because of the existence of compensation temperature. The effect of next nearest neighbour interactions on compensation temperature and phase transition have been studied by focussing on thermal response of some thermodynamic quantities using the metropolis algorithm. An effort also made to understand the role of intralayer and interlayer interactions in controlling compensation temperature and critical temperature within such a system.

关键词： Trilayered Ising lattice Monte Carlo simulation metropolis algorithm compensation temperature critical temperature magnetisation coercive field

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On equilibrium metropolis simulations on self-organized urban street networks

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APPLIED NETWORK SCIENCE 2021年第1期6卷 1-30页

作者： Benoit, Jerome G. M. Jabari, Saif Eddin G. New York Univ Abu Dhabi POB 129188 Abu Dhabi U Arab Emirates Ronin Inst Montclair NJ 07043 USA NYU Tandon Sch Engn Brooklyn NY 11201 USA

Urban street networks of unplanned or self-organized cities typically exhibit astonishing scale-free patterns. This scale-freeness can be shown, within the maximum entropy formalism (MaxEnt), as the manifestation of a fluctuating system that preserves on average some amount of information. Monte Carlo methods that can further this perspective are cruelly missing. Here we adapt to self-organized urban street networks the metropolis algorithm. The "coming to equilibrium" distribution is established with MaxEnt by taking scale-freeness as prior hypothesis along with symmetry-conservation arguments. The equilibrium parameter is the scaling;its concomitant extensive quantity is, assuming our lack of knowledge, an amount of information. To design an ergodic dynamics, we disentangle the state-of-the-art street generating paradigms based on non-overlapping walks into layout-at-junction dynamics. Our adaptation reminisces the single-spin-flip metropolis algorithm for Ising models. We thus expect metropolis simulations to reveal that self-organized urban street networks, besides sustaining scale-freeness over a wide range of scalings, undergo a crossover as scaling varies-literature argues for a small-world crossover. Simulations for Central London are consistent against the state-of-the-art outputs over a realistic range of scaling exponents. Our illustrative Watts-Strogatz phase diagram with scaling as rewiring parameter demonstrates a small-world crossover curving within the realistic window 2-3;it also shows that the state-of-the-art outputs underlie relatively large worlds. Our metropolis adaptation to self-organized urban street networks thusly appears as a scaling variant of the Watts-Strogatz model. Such insights may ultimately allow the urban profession to anticipate self-organization or unplanned evolution of urban street networks.

关键词： Urban street networks Self-organization Scale-freeness metropolis algorithm MaxEnt Symmetries Conserved quantities Self-similarity Surprisal Graph matchings Ising model Watts– Strogatz model Small-world crossover

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Velocity Driven Transition in Three Dimensional Ising Model

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INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS 2022年第5期61卷 1-11页

作者： Sahai, Manish K. Bakshi, A. K. Bhabha Atom Res Ctr Homi Bhabha Natl Inst Mumbai 400094 Maharashtra India Bhabha Atom Res Ctr BARC Radiol Phys & Advisory Div Mumbai 400094 Maharashtra India

Structure and dynamics of interface in three dimensional Ising model on a simple cubic lattice has been studied. Lattice is placed in an inhomogeneous external field, of specific profile, and field is translating with velocity V-f. For small V-f,V- magnetization interface generated by the field is pinned to the field interface. As V-f is increased magnetization interface detaches from field interface. For small V-f, the local slope of the interface locks in to one of many possible rational values which most closely approximates field profile. Accordingly, in two dimensional Ising model, plot of orientation of field interface vs. most probable local slope of magnetization interface has a staircase structure. In present case of three dimensional Ising model, these steps are manifested as patches in graphical representation. Effect of V-f on this patch structure has been studied.

关键词： Classical Monte Carlo simulation Kinetic Ising Model metropolis algorithm Moving interface

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Speedup of the metropolis protocol via algorithmic optimization

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JOURNAL OF COMPUTATIONAL SCIENCE 2023年 66卷

作者： Macias-Medri, A. E. Viswanathan, G. M. Fiore, C. E. Koehler, M. da Luz, M. G. E. Univ Fed Parana Dept Fis CP 19044 BR-81531980 Curitiba Parana Brazil Univ Fed Rio Grande do Norte Dept Phys BR-59078900 Natal RN Brazil Univ Fed Rio Grande do Norte Natl Inst Sci & Technol Complex Syst BR-59078900 Natal RN Brazil Univ Sao Paulo Inst Fis BR-05315970 Sao Paulo SP Brazil

The metropolis algorithm is widely used in Monte Carlo (MC) simulations in diverse areas of science and technology, especially for problems formulated in terms of lattice models. A common situation is the necessity to perform long sequential processing, e.g., when looking for equilibrium states of distinct physical systems. Hence, even marginal increases in efficiency of the algorithm individual steps can lead to significant reductions in absolute execution runtimes. Usual speedup procedures include hardware updates, parallelization (when possible) and sampling methods. Here we follow a different direction in trying to decrease the full execution times of MC approaches: algorithmic optimization. We show that the algorithms can be improved by implementing relatively few and simple changes in their organization and structure. First, we discuss some refinements for the pseudo-random number generator, addressing the broadly employed Mersenne-Twister algorithm (MT19937-64). Second, we develop a protocol to precalculate the Boltzmann factor, thereby avoiding the high cost of repeatedly calls to this exponential function (indeed, a very recurring step in the standard metropolis method). To benchmark our proposals we choose the Ising model since it is one of the best known and more extensively studied problems in statistical physics. We consider the mentioned optimizations and different computational elements, like compilers and Hamiltonian variables ranges, testing the efficiency to obtain the system solutions. Our results suggest that the present set of improvement schemes-namely;decreasing the processing time for both, to generate a random number and to implement the one-flip metropolis step;systematically enforcing optimization for the maximum quantity of algorithm structures accessing random numbers in a code;and considerably reducing the amount of required computations of the MC probabilistic actualization term-might constitute a relevant addition to the existing coll

关键词： metropolis algorithm Monte Carlo optimization Pseudo-random number generators Precalculated Boltzmann factor Ising model

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Singular relaxation of a random walk in a box with a metropolis Monte Carlo dynamics

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JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 2023年第25期56卷 255003-255003页

作者： Chepelianskii, Alexei D. Majumdar, Satya N. Schawe, Hendrik Trizac, Emmanuel Univ Paris Saclay CNRS Lab Phys Solides F-91405 Orsay France Univ Paris Saclay CNRS LPTMS F-91405 Orsay France CY Cergy Paris Univ LPTM UMR 8089 CNRS F-95000 Cergy France

We study analytically the relaxation eigenmodes of a simple Monte Carlo algorithm, corresponding to a particle in a box which moves by uniform random jumps. Moves outside of the box are rejected. At long times, the system approaches the equilibrium probability density, which is uniform inside the box. We show that the relaxation towards this equilibrium is unusual: for a jump length comparable to the size of the box, the number of relaxation eigenmodes can be surprisingly small, one or two. We provide a complete analytic description of the transition between these two regimes. When only a single relaxation eigenmode is present, a suitable choice of the symmetry of the initial conditions gives a localizing decay to equilibrium. In this case, the deviation from equilibrium concentrates at the edges of the box where the rejection probability is maximal. Finally, in addition to the relaxation analysis of the Master equation, we also describe the full eigen-spectrum of the Master equation including its sub-leading eigen-modes.

关键词： Monte Carlo metropolis algorithm relaxation of Markov chains

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Aging following a zero-temperature quench in the d=3 Ising model

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Physical Review E 2024年第4期109卷 044148-044148页

作者： Denis Gessert Henrik Christiansen Wolfhard Janke Institut für Theoretische Physik Universität Leipzig IPF 231101 04081 Leipzig Germany Centre for Fluid and Complex Systems Coventry University Coventry CV1 5FB United Kingdom

Aging in phase-ordering kinetics of the d=3 Ising model following a quench from infinite to zero temperature is studied by means of Monte Carlo simulations. In this model the two-time spin-spin autocorrelator Cag is expected to obey dynamical scaling and to follow asymptotically a power-law decay with the autocorrelation exponent λ. Previous work indicated that the lower Fisher-Huse bound of λ≥d/2=1.5 is violated in this model. Using much larger systems than previously studied, the instantaneous exponent for λ we obtain at late times does not disagree with this bound. By conducting systematic fits to the data of Cag using different Ansätze for the leading correction term, we find λ=1.58(14), with most of the error attributed to the systematic uncertainty regarding the Ansätze. This result is in contrast to the recent report that below the roughening transition universality might be violated.

关键词： Aging Dynamical phase transitions Nonequilibrium statistical mechanics Nonequilibrium lattice models Nonequilibrium systems Heatbath algorithm Ising model metropolis algorithm Monte Carlo methods Spin lattice models

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Exact Calculation of the Probabilities of Rare Events in Cluster-Cluster Aggregation

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Physical Review Letters 2024年第9期133卷 097101页

作者： R. Rajesh V. Subashri Oleg Zaboronski C.I.T. Campus Taramani Chennai 600113 India Training School Complex Anushakti Nagar Mumbai 400094 India Mathematics Institute

We develop an action formalism to calculate probabilities of rare events in cluster-cluster aggregation for arbitrary collision kernels and establish a pathwise large deviation principle with total mass being the rate. As an application, the rate function for the number of surviving particles as well as the optimal evolution trajectory are calculated exactly for the constant, sum, and product kernels. For the product kernel, we argue that the second derivative of the rate function has a discontinuity. The theoretical results agree with simulations tailored to the calculation of rare events.

关键词： Growth processes Irreversible processes Nonequilibrium statistical mechanics Phase transitions Polymers Exact solutions for many-body systems Large deviation & rare event statistics Master equation metropolis algorithm Monte Carlo methods Path-integral methods Scaling methods

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Comparison of integral equation theories of the liquid state

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Physical Review E 2024年第4期110卷 044608页

作者： Ilian Pihlajamaa Liesbeth M. C. Janssen Soft Matter &amp Biological Physics Department of Applied Physics <a href="https://***/02c2kyt77">Eindhoven University of Technology</a> P.O. Box 513 5600MB Eindhoven The Netherlands.

The Ornstein-Zernike equation is a powerful tool in liquid state theory for predicting structural and thermodynamic properties of fluids. Combined with a suitable closure, it has been shown to reproduce, e.g., the static structure factor, pressure, and compressibility of liquids to a great degree of accuracy. However, out of the multitude of closures that exist for the Ornstein-Zernike equation, it is hard to predict a priori which closure will give the most accurate predictions for the system at hand. To alleviate this problem, we compare the predictive power of many closures on a curated set of representative benchmark systems, including those with hard-sphere, inverse power-law, Gaussian core, and Lennard-Jones particles, in three and two dimensions. For example, we find that the well-known and highly used Percus-Yevick closure gives significantly worse predictions than lesser-known closures of equal complexity in all cases studied. We anticipate that the trends observed in our results will aid in making more informed decisions regarding closure choices. To facilitate the adoption of more modern closure theories, we also have packaged, documented, and distributed the code necessary to numerically solve the equations for a given closure and pair interaction potential.

关键词： Classical statistical mechanics Thermodynamics Classical fluids Liquids Approximation methods for many-body systems metropolis algorithm Monte Carlo methods Virial theorem

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Optical Kinetic Theory of Nonlinear Multimode Photonic Networks

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Physical Review Letters 2024年第19期132卷 193802-193802页

作者： Arkady Kurnosov Lucas J. Fernández-Alcázar Alba Ramos Boris Shapiro Tsampikos Kottos Department of Physics Wave Transport in Complex Systems Laboratory Wesleyan University Middletown Connecticut 06459 USA Institute for Modeling and Innovative Technology IMIT (CONICET - UNNE) Corrientes W3404AAS Argentina Physics Department Natural and Exact Science Faculty Northeastern University of Argentina Corrientes W3404AAS Argentina Technion - Israel Institute of Technology Technion City Haifa 3200 Israel

Recent experimental developments in multimode nonlinear photonic circuits (MMNPCs), have motivated the development of an optical thermodynamic theory that describes the equilibrium properties of an initial beam excitation. However, a nonequilibrium transport theory for these systems, when they are in contact with thermal reservoirs, is still terra incognita. Here, by combining Landauer and kinematics formalisms we develop a universal one-parameter scaling theory that describes the whole transport behavior from the ballistic to the diffusive regime, including both positive and negative optical temperature scenarios. We also derive a photonic version of the Wiedemann-Franz law that connects the thermal and power conductivities. Our work paves the way toward a fundamental understanding of the transport properties of MMNPCs and may be useful for the design of all-optical cooling protocols.

关键词： Classical optics Kinetic theory Nonequilibrium & irreversible thermodynamics Nonlinear optics Optics & lasers Transport phenomena Nonequilibrium lattice models Nonequilibrium systems Optical fibers Waveguides Data analysis Finite-size scaling Linear response theory metropolis algorithm Monte Carlo methods Scaling methods Schroedinger equation

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Thermodynamics of the Quantum Mpemba Effect

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Physical Review Letters 2024年第14期133卷 140404页

作者： Mattia Moroder Oisín Culhane Krissia Zawadzki John Goold Department of Physics Arnold Sommerfeld Center for Theoretical Physics (ASC) Munich Center for Quantum Science and Technology (MCQST) School of Physics Instituto de Física de São Carlos Universidade de São Paulo CP 369 13560-970 São Carlos São Paulo Brazil Trinity Quantum Alliance Unit 16 Trinity Technology and Enterprise Centre Pearse Street Dublin 2 D02YN67

We investigate the quantum Mpemba effect from the perspective of nonequilibrium quantum thermodynamics by studying relaxation dynamics of quantum systems coupled to a Markovian heat bath, which are described by Davies maps. Starting from a state with coherences in the energy eigenbasis, we demonstrate that an exponential speedup to equilibrium will always occur if the state is transformed to a diagonal state in the energy eigenbasis, provided that the spectral gap of the generator is defined by a complex eigenvalue. When the transformed state has a higher nonequilibrium free energy, we argue using thermodynamic reasoning that this is a genuine quantum Mpemba effect. Furthermore, we show how a unitary transformation on an initial state can always be constructed to yield the effect and demonstrate our findings by studying the dynamics of both the nonequilibrium free energy and the irreversible entropy production in single and multiqubit examples.

关键词： Entropy production Nonequilibrium & irreversible thermodynamics Open quantum systems Quantum thermodynamics Nonequilibrium systems Quantum spin models Exact diagonalization Lindblad equation Master equation metropolis algorithm Numerical approximation & analysis

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