Renormalization group study of the two-dimensional random transverse-field Ising model

TL;DR

This study employs an advanced numerical strong disorder renormalization group approach to analyze the critical behavior of the two-dimensional random transverse-field Ising model, confirming the universality of its infinite disorder fixed point and critical exponents.

Contribution

It provides improved estimates of critical exponents and demonstrates the universality of the infinite disorder fixed point across different disorder types using large-scale simulations.

Findings

Critical exponent nu = 1.24(2) for sample-dependent pseudo-critical points.

Universal critical exponents x = 0.982(15) and psi = 0.48(2) across disorder types.

Scaling behavior of magnetization and dynamical scaling in Griffiths phases.

Abstract

The infinite disorder fixed point of the random transverse-field Ising model is expected to control the critical behavior of a large class of random quantum and stochastic systems having an order parameter with discrete symmetry. Here we study the model on the square lattice with a very efficient numerical implementation of the strong disorder renormalization group method, which makes us possible to treat finite samples of linear size up to $L=2048$. We have calculated sample dependent pseudo-critical points and studied their distribution, which is found to be characterized by the same shift and width exponent: $\nu=1.24(2)$. For different types of disorder the infinite disorder fixed point is shown to be characterized by the same set of critical exponents, for which we have obtained improved estimates: $x=0.982(15)$ and $\psi=0.48(2)$. We have also studied the scaling behavior of the magnetization in the vicinity of the critical point as well as dynamical scaling in the ordered and disordered Griffiths phases.