Phase transition in the three-dimensional O(N)⊗ O(M) model: a Monte Carlo study

2022/05/15 by A. O. Sorokin, Sorokin, A. O.
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Quantum Chromodynamics and Particle Interactions #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2205.07199

openalex publication_date 2022/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using Monte Carlo simulations, we consider the lattice version of the O(N)⊗ O(M) sigma model for 2≤ M≤4 and M≤ N ≤8. We find a continuous transition for N≥ M+4. Estimates of the critical exponents for cases of second-order and weak first-order transitions are found. For M=2 our estimates of the exponents and marginal dimensionality N_c⁺(M) are in good agreement with the results of the non-perturbative renormalization group approach. For M≥2 we find estimates of the exponents and marginal dimensionality between the values obtained in the first and second orders of the large-N expansion. To complete the picture, we also consider the usual O(N) model (M=1).

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