Progress in numerical simulations of systems with a $\theta-$vacuum like term: The two and three-dimensional Ising model within an imaginary magnetic field

TL;DR

This paper advances numerical simulation techniques to analyze the antiferromagnetic Ising model with imaginary magnetic fields in two and three dimensions, revealing complex phase structures and validating mean-field approximations.

Contribution

It successfully reconstructs the behavior of the Ising model with imaginary magnetic fields in low dimensions and compares results with mean-field predictions, highlighting complex phase structures.

Findings

Qualitative agreement between mean-field and low-dimensional results

Reconstruction of the model's behavior in low temperature regime

Identification of complex phase structures in the model

Abstract

Using the approach developed in \cite{REFVIC2}, we succeeded in reconstructing the behaviour of the antiferromagnetic Ising model with imaginary magnetic field $i\theta$ for two and three dimensions in the low temperature regime. A mean-field calculation, expected to work well for high dimensions, is also carried out, and the mean-field results coincide qualitatively with those of the two- and three-dimensional Ising model. The mean field analysis reveals also a phase structure more complex than the one expected for $QCD$ with a topological $\theta-$therm.