The O(n) loop model on a three-dimensional lattice

TL;DR

This paper investigates a class of three-dimensional loop models with varying parameters, using Monte Carlo simulations to determine critical points and exponents, confirming their relation to the 3D O(n) universality class.

Contribution

It introduces efficient worm algorithms for studying 3D loop models across multiple n values and provides new estimates of critical exponents.

Findings

Critical points identified for various n values.

Estimated critical exponents match known 3D O(n) universality class values.

Worm algorithms show high efficiency with low dynamic exponent z.

Abstract

We study a class of loop models, parameterized by a continuously varying loop fugacity n, on the hydrogen-peroxide lattice, which is a three-dimensional cubic lattice of coordination number 3. For integer n > 0, these loop models provide graphical representations for n-vector models on the same lattice, while for n = 0 they reduce to the self-avoiding walk problem. We use worm algorithms to perform Monte Carlo studies of the loop model for n = 0, 0.5, 1, 1.5, 2, 3, 4, 5 and 10 and obtain the critical points and a number of critical exponents, including the thermal exponent yt, magnetic exponent yh, and loop exponent yl. For integer n, the estimated values of yt and yh are found to agree with existing estimates for the three-dimensional O(n) universality class. The efficiency of the worm algorithms is reflected by the small value of the dynamic exponent z, determined from our analysis of the integrated autocorrelation times.