Universal Reduction of Effective Coordination Number in the Quasi-One-Dimensional Ising Model

TL;DR

This paper investigates the critical temperature of quasi-one-dimensional Ising ferromagnets, revealing a universal reduction in effective coordination number in the weak coupling regime, independent of spin size, and linking it to a quantum critical point.

Contribution

It demonstrates that the effective coordination number in quasi-1D Ising models is universally reduced and independent of spin size, connecting it to the quantum critical point of a transverse-field Ising model.

Findings

Critical temperature follows a chain mean-field formula with reduced coordination.

Effective coordination number is independent of spin size.

In the weak coupling limit, it equals the quantum critical point of a spin-1/2 transverse-field Ising model.

Abstract

Critical temperature of quasi-one-dimensional general-spin Ising ferromagnets is investigated by means of the cluster Monte Carlo method performed on infinite-length strips, L times infty or L times L times infty. We find that in the weak interchain coupling regime the critical temperature as a function of the interchain coupling is well-described by a chain mean-field formula with a reduced effective coordination number, as the quantum Heisenberg antiferromagnets recently reported by Yasuda et al. [Phys. Rev. Lett. 94, 217201 (2005)]. It is also confirmed that the effective coordination number is independent of the spin size. We show that in the weak interchain coupling limit the effective coordination number is, irrespective of the spin size, rigorously given by the quantum critical point of a spin-1/2 transverse-field Ising model.