Computation of microcanonical entropy at fixed magnetization without direct counting
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.
Cite
@article{arxiv.2107.12742,
title = {Computation of microcanonical entropy at fixed magnetization without direct counting},
author = {Alessandro Campa and Giacomo Gori and Vahan Hovhannisyan and Stefano Ruffo and Andrea Trombettoni},
journal= {arXiv preprint arXiv:2107.12742},
year = {2021}
}
Comments
41 pages, 9 figures, in press in Journal of Statistical Physics