Broad Histogram Method for Multiparametric Hamiltonians

TL;DR

This paper extends the Broad Histogram Method to calculate spectral degeneracies in multiparametric Hamiltonians, successfully determining entire critical lines for complex Ising models from a single simulation.

Contribution

The paper introduces an extension of the Broad Histogram Method to handle multiparametric Hamiltonians, enabling efficient computation of critical lines in complex systems.

Findings

Successfully obtained critical lines for Ising models with multiple interactions

Demonstrated the method's accuracy and efficiency

Achieved results from a single computer run

Abstract

We extended the Broad Histogram Method in order to obtain spectral degeneracies for systems with multiparametric Hamiltonians. As examples we obtained the critical lines for the square lattice Ising model with nearest and next-nearest neighbor interactions and the antiferromagnetic Ising model in an external field. For each system, the entire critical line is obtained using data from a single computer run. We also discuss the accuracy and efficiency of our method.