Computation of Microcanonical Entropy at Fixed Magnetization Without Direct Counting
Year: 2021
Authors: Campa A., Gori G., Hovhannisyan V., Ruffo S., Trombettoni A.
Autors Affiliation: Ist Super Sanita, Natl Ctr Radiat Protect & Computat Phys, Viale Regina Elena 299, I-00161 Rome, Italy; Heidelberg Univ, Inst Theoret Phys, D-69120 Heidelberg, Germany; AI Alikhanyan Natl Sci Lab, 2 Alikhanian Bros St, Yerevan 0036, Armenia; SISSA, Via Bonomea 265, I-34136 Trieste, Italy; Ist Nazl Fis Nucl, Sez Trieste, I-34151 Trieste, Italy; CNR, Ist Sistemi Complessi, Via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy; Univ Trieste, Dept Phys, Str Costiera 11, I-34151 Trieste, Italy; CNR IOM DEMOCRITOS Simulat Ctr, Via Bonomea 265, I-34136 Trieste, Italy.
Abstract: We discuss a method to compute the microcanonical entropy at fixed magnetization without direct counting. Our approach is based on the evaluation of a saddle-point leading to an optimization problem. The method is applied to a benchmark Ising model with simultaneous presence of mean-field and nearest-neighbour interactions for which direct counting is indeed possible, thus allowing a comparison. Moreover, we apply the method to an Ising model with mean-field, nearest-neighbour and next-nearest-neighbour interactions, for which direct counting is not straightforward. For this model, we compare the solution obtained by our method with the one obtained from the formula for the entropy in terms of all correlation functions. This example shows that for general couplings our method is much more convenient than direct counting methods to compute the microcanonical entropy at fixed magnetization.
Journal/Review: JOURNAL OF STATISTICAL PHYSICS
Volume: 184 (2) Pages from: 21-1 to: 21-36
More Information: Discussions with N. Defenu, D. Mukamel and N. Ananikian are gratefully acknowledged. A.C. acknowledges financial support from INFN (Istituto Nazionale di Fisica Nucleare) through the projects DYNSYSMATH and ENESMA. G .G. is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) underGermany’s Excellence StrategyEXC2181/1 -390900948 (the Heidelberg STRUCTURES Excellence Cluster). The authors acknowledge support by the RA MES Science Committee and National Research Council of the Republic of Italy in the frames of the joint research Project No. SCS 19IT-008 and Statistical Physics of Classical and Quantum Non Local Hamiltonians: Phase Diagrams and Renormalization Group. This work is part of MUR-PRIN2017 Project Coarse-grained description for nonequilibrium systems and transport phenomena (CO-NEST) No. 201798CZL whose partial financial support is acknowledged.KeyWords: Entropy; Long-range interactions; Ensemble inequivalence; Phase transitions; 82B05; 82B26DOI: 10.1007/s10955-021-02809-yCitations: 3data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2025-09-07References taken from IsiWeb of Knowledge: (subscribers only)
