Statistics of lowest excitations in two dimensional Gaussian spin glasses

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.

4 pages, 3 figures, (v2) revised version, (v3) corrected typos

References in corpus (9)

• Lower Critical Dimension of Ising Spin Glasses
• Aspect-Ratio Scaling and The Stiffness Exponent $\theta$ for Ising Spin Glasses
• The stiffness exponent of two-dimensional Ising spin glasses for non-periodic boundary conditions using aspect-ratio scaling
• Large-Scale, Low-Energy Excitations in the Two-Dimensional Ising Spin Glass
• Anderson Orthogonality Catastrophe in Disordered Systems
• Corrections to Scaling are Large for Droplets in Two-Dimensional Spin Glasses
• Non-compact local excitations in spin glasses
• Corrections to scaling in the droplet picture of spin glasses
• Random energy levels and low-temperature expansions for spin glasses

Cited by in corpus (8)

• Low-temperature behavior of two-dimensional Gaussian Ising spin glasses
• Large-Scale, Low-Energy Excitations in the Two-Dimensional Ising Spin Glass
• Thermal fluctuations in pinned elastic systems: field theory of rare events and droplets
• Generating droplets in two-dimensional Ising spin glasses by using matching algorithms
• The droplet-scaling versus replica symmetry breaking debate in spin glasses revisited
• Statistics of low energy excitations for the directed polymer in a $1+d$ random medium ($d=1,2,3$)
• Random field Ising model : statistical properties of low-energy excitations and of equilibrium avalanches
• Energetics of clusters in the two-dimensional Ising spin glass