Probing the Critical Behavior of a Sign-Problematic Model with Monte Carlo Simulations

TL;DR

This paper investigates the critical behavior of a sign-problematic model using Monte Carlo simulations, revealing limitations of traditional sign measures and proposing a universal approach to study phase transitions.

Contribution

It introduces a novel framework leveraging universality and finite-size scaling to analyze phase transitions in models with sign problems, validated through Monte Carlo simulations.

Findings

Average sign peaks near critical points but is not a definitive indicator.

Modified average sign effectively probes phase transitions.

Universal properties can be studied via related reference models.

Abstract

The sign-problematic generalized Baxter-Wu (GBW) model with asymmetric complex couplings is mapped onto a one-dimensional quantum model. Utilizing the model's exactly known critical properties, we study the relation between the conventional and the modified average signs and the phase transitions in the GBW model. We find that the average sign develops a negative peak near the critical point, but it is not a unique indicator of phase transition, as similar features can appear in non-critical regions. While the average modified sign provides a viable probe for the phase transition, the practical effectiveness of this method is limited by the exponential scaling of computational cost with the system's volume. We propose that the universal properties of the original model can be investigated through simulating the related reference model, based on the universality assumption. Using finite-size scaling analysis based on Monte Carlo simulations, we confirm the validity of this method, which thereby provides a novel framework for investigating phase transitions in systems plagued by the sign problem.