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

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.

22 pages, 7 figures

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• Boundary Criticality of the 3D O($N$) Model: From Normal to Extraordinary
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• Caution on emergent continuous symmetry: a Monte Carlo investigation of transverse-field frustrated Ising model on triangle and honeycomb lattices
• Surface criticality of antiferromagnetic Potts model
• Worm-algorithm-type Simulation of Quantum Transverse-Field Ising Model
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• Special Transition and Extraordinary Phase on the Surface of a Two-Dimensional Quantum Heisenberg Antiferromagnet
• Universal Critical Wrapping Probabilities in the Canonical Ensemble
• Backbone and shortest-path exponents of the two-dimensional $Q$-state Potts model
• The tricritical Ising CFT and conformal bootstrap
• Simulating the All-Order Strong Coupling Expansion V: Ising Gauge Theory
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• Completely packed O($n$) loop models and their relation with exactly solved coloring models
• Finite-Size Scaling of the High-Dimensional Ising Model in the Loop Representation
• Anomalous dimensions from conformal field theory: Generalized ${\varphi }^{2n+1}$ theories
• Ising-like phase transition of an n-component Eulerian face-cubic model
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• Ising models on the hydrogen peroxide and other lattices