Scaling behavior of the four-point renormalized coupling constant in the two dimensional O(2) and O(3) non-linear sigma models

TL;DR

This study uses Monte Carlo simulations to analyze the scaling behavior of the four-point renormalized coupling constant in two-dimensional O(2) and O(3) non-linear sigma models, revealing critical properties and hyperscaling.

Contribution

It provides thermodynamic values of the four-point coupling constant in the continuum limit for these models, demonstrating the vanishing of the critical index and confirming hyperscaling.

Findings

Critical index of the coupling constant vanishes

Evidence of hyperscaling in both models

Thermodynamic values obtained via Monte Carlo simulations

Abstract

We report thermodynamic values of four-point renormalized coupling constant calculated by Monte Carlo simulations in the continuum limits of the lattice versions of the two-dimensional O(2) and O(3) non-linear sigma models. In each case the critical index of the coupling constant vanishes, which leads to hyperscaling (non-triviality).