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arXiv:hep-th/0506241 · International Journal of Modern Physics B

MONTE–CARLO THERMODYNAMIC BETHE ANSATZ

Doron Gepner

Published May 23, 2006• 0 citations
arXivHTMLPDF

Abstract

We introduce a Monte–Carlo simulation approach to thermodynamic Bethe ansatz (TBA). We exemplify the method on one-particle integrable models, which include a free boson and a free fermions systems along with the scaling Lee–Yang model (SLYM). It is confirmed that the central charges and energies are correct to a very good precision, typically 0.1% or so. The advantage of the method is that it allows the calculation of all the dimensions and even the particular partition function.

DOI
10.1142/s0217979206034522

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Presented is a method, which we call Bethe ansatz cluster expansion (BACE) method, to investigate statistical mechanics of quantum integrable systems. By use of only the Bethe ansatz equation, n -particle partition functions are exactly calculated. From the expression for the partition function, the n -particle cluster integrals are derived. The results completely agree with those of the thermal Bethe ansatz (TBA) by Yang and Yang. Thus, the BACE method directly proves the validity of the TBA. Partition theory and graphical representation are used to make the presentation simple and transparent.