Two dimensional SU(N) x SU(N) chiral models on the lattice

TL;DR

This paper investigates two-dimensional SU(N) x SU(N) chiral models on the lattice using strong and weak coupling expansions and numerical simulations, providing detailed results on energy, beta functions, and scaling behavior.

Contribution

It presents the first 12th order strong coupling series for all N ≥ 6 and compares numerical results with theoretical predictions, enhancing understanding of lattice SU(N) x SU(N) models.

Findings

Strong coupling series up to 12th order for all N ≥ 6.

Numerical confirmation of faster approach to asymptopia in the energy scheme.

Agreement of mass ratios at N=6 with exact S-matrix predictions within 1%.

Abstract

Lattice $SU(N)\times SU(N)$ chiral models are analyzed by strong and weak coupling expansions and by numerical simulations. $12^{th}$ order strong coupling series for the free and internal energy are obtained for all $N\geq 6$. Three loop contributions to the internal energy and to the lattice $\beta$-function are evaluated for all $N$ and non-universal corrections to the asymptotic $\Lambda$ parameter are computed in the ``temperature'' and the ``energy'' scheme. Numerical simulations confirm a faster approach to asymptopia of the energy scheme. A phenomenological correlation between the peak in the specific heat and the dip of the $\beta$-function is observed. Tests of scaling are performed for various physical quantities, finding substantial scaling at $\xi \gtrsim 2$. In particular, at $N=6$ three different mass ratios are determined numerically and found in agreement, within statistical errors of about 1\%, with the theoretical predictions from the exact S-matrix theory.