Transverse-spin correlations of the random transverse-field Ising model

TL;DR

This paper investigates the critical transverse-spin correlations in the random transverse-field Ising model across one to three dimensions, revealing an algebraic decay characterized by a dimension-dependent exponent, using SDRG and numerical methods.

Contribution

It extends the analysis of the random transverse-field Ising model by calculating the transverse-spin correlation function in multiple dimensions with numerical SDRG.

Findings

Transverse-spin correlations decay algebraically with distance.

Decay exponent approximately equals 2+2d in d dimensions.

Results in 1D relate to dimer-dimer correlations in the AF XX-chain.

Abstract

The critical behavior of the random transverse-field Ising model in finite dimensional lattices is governed by infinite disorder fixed points, several properties of which have already been calculated by the use of the strong disorder renormalization group (SDRG) method. Here we extend these studies and calculate the connected transverse-spin correlation function by a numerical implementation of the SDRG method in $d=1,2$ and $3$ dimensions. At the critical point an algebraic decay of the form $\sim r^{-\eta_t}$ is found, with a decay exponent being approximately $\eta_t \approx 2+2d$. In $d=1$ the results are related to dimer-dimer correlations in the random AF XX-chain and have been tested by numerical calculations using free-fermionic techniques.