3D Unoriented loop models and the RP^n-1 sigma model

2021/07/28 by Pablo Serna, Serna, Pablo
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el) #cond-mat.stat-mech #cond-mat.str-el

paper · pdf · doi:10.48550/arxiv.2107.13366

openalex publication_date 2021/07/28 · arxiv created 2021/09/01 · arxiv updated 2021/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a completely-packed loop model with crossings in a three-dimensional lattice and confirm it is described by RP^n-1 sigma field theories. We use Monte Carlo simulations, with systems sizes up to 1800×1800×1800, to obtain the critical exponents for a universality class with no previously reported estimates in the literature, namely the replica-like limit n→1 of RP^n-1 sigma field theory. Estimates of critical exponents include ν=0.918(5) and η=-0.091(9). We also study the scaling dimension of the 4-leg watermelon correlators, particularly for n=1 we obtain the value x₄=1.292(8).

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