Statistics of lowest excitations in two dimensional Gaussian spin glasses

TL;DR

This paper investigates the statistics of lowest excitations in 2D Gaussian spin glasses, introducing a new zero-temperature exponent that relates to the thermal exponent, providing a novel measurement method and challenging existing theories.

Contribution

It introduces a new zero-temperature exponent lambda that relates finite-volume and large-scale excitations, offering a novel way to measure the thermal exponent theta without assumptions.

Findings

Existence of a new zero-temperature exponent lambda.

Theta is less than theta_{DW}, indicating MacMillan excitations are atypical.

Provides a new method to measure theta directly from excitation statistics.

Abstract

A detailed investigation of lowest excitations in two-dimensional Gaussian spin glasses is presented. We show the existence of a new zero-temperature exponent lambda describing the relative number of finite-volume excitations with respect to large-scale ones. This exponent yields the standard thermal exponent of droplet theory theta through the relation, theta=d(lambda-1). Our work provides a new way to measure the thermal exponent theta without any assumption about the procedure to generate typical low-lying excitations. We find clear evidence that theta < theta_{DW} where theta_{DW} is the thermal exponent obtained in domain-wall theory showing that MacMillan excitations are not typical.