Universal and non-universal amplitude ratios for scaling corrections on Ising strips

TL;DR

This paper investigates finite-size scaling corrections in critical Ising strips, revealing universal amplitude ratios for certain parameters under specific conditions, and how these ratios change with anisotropy, spin, and interaction range.

Contribution

It provides exact and numerical analysis of amplitude ratios in Ising strips, identifying conditions for their universality and how they vary with system parameters.

Findings

Ratios $b_k/a_k$ are universal for $S=1/2$ with first-neighbor couplings.

Universality of ratios does not hold when changing spin $S$ or interaction range.

Amplitude ratios depend on boundary conditions and system anisotropy.

Abstract

We consider strips of Ising spins at criticality. For strips of width $N$ sites, subdominant (additive) finite-size corrections to scaling are assumed to be of the form $a_k/N^k$ for the free energy, and $b_k/N^k$ for inverse correlation length, with integer values of $k$. We investigate the set $\{a_k,b_k\}$ ($k \geq 2$) by exact evaluation and numerical transfer-matrix diagonalization techniques, and their changes upon varying anisotropy of couplings, spin quantum number $S$, and (finite) interaction range, in all cases for both periodic (PBC) and free (FBC) boundary conditions across the strip. We find that the coefficient ratios $b_k/a_k$ remain constant upon varying coupling anisotropy for $S=1/2$ and first-neighbor couplings, for both PBC and FBC (albeit at distinct values in either case). Such universal behavior is not maintained upon changes in $S$ or interaction range.