Universality of the glassy transitions in the two-dimensional +- J Ising model

TL;DR

This study demonstrates the universality of glassy transitions in the 2D +- J Ising model across different bond distributions, highlighting the independence of critical behavior from the specific p value and analyzing finite-size scaling challenges.

Contribution

It provides evidence that the glassy critical behavior in the 2D +- J Ising model is universal across a range of p values and discusses finite-size scaling methods suitable for zero-temperature glassy transitions.

Findings

Glassy critical behavior is universal for p between 1-p_0 and p_0.

Glassy and magnetic modes are decoupled at the multicritical zero-temperature point.

Finite-size scaling should use ξ/L instead of TL^{1/ν} due to freezing phenomena.

Abstract

We investigate the zero-temperature glassy transitions in the square-lattice +- J Ising model, with bond distribution $P(J_{xy}) = p \delta(J_{xy} - J) + (1-p) \delta(J_{xy} + J)$; p=1 and p=1/2 correspond to the pure Ising model and to the Ising spin glass with symmetric bimodal distribution, respectively. We present finite-temperature Monte Carlo simulations at p=4/5, which is close to the low-temperature paramagnetic-ferromagnetic transition line located at p=0.89, and at p=1/2. Their comparison provides a strong evidence that the glassy critical behavior that occurs for $1-p_0<p<p_0$, $p_0=0.897$, is universal, i.e., independent of p. Moreover, we show that glassy and magnetic modes are not coupled at the multicritical zero-temperature point where the paramagnetic-ferromagnetic transition line and the T=0 glassy transition line meet. On the theoretical side we discuss the validity of finite-size scaling in glassy systems with a zero-temperature transition and a discrete Hamiltonian spectrum. Because of a freezing phenomenon which occurs in a finite volume at sufficiently low temperatures, the standard finite-size scaling limit in terms of $TL^{1/\nu}$ does not exist: the renormalization-group invariant quantity $\xi/L$ should be used instead as basic variable.