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Computation of microcanonical entropy at fixed magnetization without direct counting

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 neares...

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Bibliographic Details
Main Authors: Campa, Alessandro (Author) , Gori, Giacomo (Author) , Hovhannisyan, Vahan (Author) , Ruffo, Stefano (Author) , Trombettoni, Andrea (Author)
Format: Article (Journal)
Language:English
Published: 5 August 2021
In: Journal of statistical physics
Year: 2021, Volume: 184, Issue: 2, Pages: 1-36
ISSN:1572-9613
DOI:10.1007/s10955-021-02809-y
Online Access:Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1007/s10955-021-02809-y
Verlag, lizenzpflichtig, Volltext: https://link.springer.com/article/10.1007%2Fs10955-021-02809-y
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Author Notes:Alessandro Campa · Giacomo Gori · Vahan Hovhannisyan · Stefano Ruffo · Andrea Trombettoni
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Summary: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.
Item Description:Gesehen am 08.11.2021
Physical Description:Online Resource
ISSN:1572-9613
DOI:10.1007/s10955-021-02809-y

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