ϕ^{4} lattice model with cubic symmetry in three dimensions: Renormalization group flow and firstorder phase transitions
Abstract
We study the threecomponent ϕ^{4} model on the simple cubic lattice in the presence of a cubic perturbation. To this end, we perform Monte Carlo simulations in conjunction with a finitesize scaling analysis of the data. The analysis of the renormalization group (RG) flow of a dimensionless quantity provides us with the accurate estimate Y_{4}−ω_{2}=0.000 81 (7 ) for the difference of the RG eigenvalue Y_{4} at the O(3 ) symmetric fixed point and the correction exponent ω_{2} at the cubic fixed point. We determine an effective exponent ν_{eff} of the correlation length that depends on the strength of the breaking of the O(3 ) symmetry. Field theory predicts that depending on the sign of the cubic perturbation, the RG flow is attracted by the cubic fixed point, or runs to an ever increasing amplitude, indicating a fluctuationinduced firstorder phase transition. We demonstrate directly the firstorder nature of the phase transition for a sufficiently strong breaking of the O(3) symmetry. We obtain accurate results for the latent heat, the correlation length in the disordered phase at the transition temperature, and the interface tension for interfaces between one of the ordered phases and the disordered phase. We study how these quantities scale with the RG flow, allowing quantitative predictions for weaker breaking of the O(3 ) symmetry.
 Publication:

Physical Review B
 Pub Date:
 February 2024
 DOI:
 10.1103/PhysRevB.109.054420
 arXiv:
 arXiv:2307.05165
 Bibcode:
 2024PhRvB.109e4420H
 Keywords:

 High Energy Physics  Lattice;
 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory
 EPrint:
 47 pages, 7 Figures