On Spin Systems with Quenched Randomness: Classical and Quantum

TL;DR

This paper proves that quenched randomness smooths out first order phase transitions in classical and quantum spin systems in low dimensions, preventing abrupt changes in order parameters like magnetization.

Contribution

It establishes a general framework showing the continuous differentiability of free energy and ground state energy in low-dimensional disordered spin systems, extending to quantum cases.

Findings

Absence of first order transitions in 2D classical systems with randomness.

No discontinuities in order parameters like magnetization in low-dimensional quantum systems.

Applicability to systems with continuous symmetry breaking in dimensions up to 4.

Abstract

The rounding of first order phase transitions by quenched randomness is stated in a form which is applicable to both classical and quantum systems: The free energy, as well as the ground state energy, of a spin system on a $d$-dimensional lattice is continuously differentiable with respect to any parameter in the Hamiltonian to which some randomness has been added when $d \leq 2$. This implies absence of jumps in the associated order parameter, e.g., the magnetization in case of a random magnetic field. A similar result applies in cases of continuous symmetry breaking for $d \leq 4$. Some questions concerning the behavior of related order parameters in such random systems are discussed.