On the Use of Finite-Size Scaling to Measure Spin-Glass Exponents

TL;DR

This paper critiques the use of finite-size scaling in spin glasses, highlighting that improper assumptions about length scales can lead to incorrect measurement of critical exponents.

Contribution

It demonstrates that replacing the correlation length with its asymptotic form in FSS can produce misleading results, emphasizing the need for all length scales to be large.

Findings

Incorrect exponents can result from improper FSS assumptions

Proper scale separation is crucial for accurate exponent measurement

FSS analysis may give false confidence in scaling collapses

Abstract

Finite-size scaling (FSS) is a standard technique for measuring scaling exponents in spin glasses. Here we present a critique of this approach, emphasizing the need for all length scales to be large compared to microscopic scales. In particular we show that the replacement, in FSS analyses, of the correlation length by its asymptotic scaling form can lead to apparently good scaling collapses with the wrong values of the scaling exponents.