Finite-Size analysis of the 4-d abelian surface gauge model

TL;DR

This paper analyzes the finite-size effects of the 4D abelian surface gauge model, confirming its second order phase transition and critical exponents consistent with mean field theory, using Monte Carlo simulations.

Contribution

It provides the first detailed finite-size scaling analysis of the 4D abelian surface gauge model, confirming its critical behavior and duality with the 4D Ising model.

Findings

Critical coupling $eta_c$ matches duality predictions.

Critical exponents $ u=1/2$ and $eta=0$ are confirmed.

Finite size effects influence the observed double peak in energy histograms.

Abstract

We present the results of a finite-size analysis of the four dimensional abelian surface gauge model. This model is defined assigning abelian variables to the plaquettes of an hypercubical lattice, and is dual to the four dimensional Ising model. This last model is known to present a second order phase transition with mean field critical exponents. We have performed Monte Carlo simulations on several lattice sizes and high statistics. The analysis of the partition function zeroes and the specific heat scaling behaviour allowed us to estimate the critical coupling $\beta_c$ as well as the critical exponents $\nu$ and $\alpha$. Our results are consistent with the second order critical exponents $\nu = 1/2$ and $\alpha = 0$. The $\beta_c$ value is in perfect agreement with duality predictions from the 4-d Ising model. Nevertheless, the energy histograms show a seemingly non-vanishing double peak structure. The interface tension analysis suggests that this may be a finite size effect.