Local vs. global variables for spin glasses

Charles M. Newman, Daniel L. Stein

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We discuss a framework for understanding why spin glasses differ so remarkably from homogeneous systems like ferromagnets, in the context of the sharply divergent low temperature behavior of short- and infinite-range versions of the same model. Our analysis is grounded in understanding the distinction between two broad classes of thermodynamic variables-those that describe the global features of a macroscopic system, and those that describe, or are sensitive to, its local features. In homogeneous systems both variables generally behave similarly, but this is not at all so in spin glasses. In much of the literature these two different classes of variables were commingled and confused. By analyzing their quite different behaviors in finite- and infinite-range spin glass models, we see the fundamental reason why the two systems possess very different types of low-temperature phases. In so doing, we also reconcile apparent discrepancies between the infinite-volume limit and the behavior of large, finite volumes, and provide tools for understanding inhomogeneous systems in a wide array of contexts. We further propose a set of "global variables" that are definable and sensible for both short-range and infinite-range spin glasses, and allow a meaningful basis for comparison of their low-temperature properties.

Original languageEnglish (US)
Title of host publicationSpin Glasses
PublisherSpringer Verlag
Pages145-158
Number of pages14
ISBN (Print)3540409025, 9783540409021
DOIs
StatePublished - 2007

Publication series

NameLecture Notes in Mathematics
Volume1900
ISSN (Print)0075-8434

Keywords

  • Domain walls
  • Edwards-Anderson model
  • Interfaces
  • Mean-field theory
  • Metastates
  • Pure states
  • Replica symmetry breaking
  • Sherrington-Kirkpatrick model
  • Spin glass

ASJC Scopus subject areas

  • Algebra and Number Theory

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    Newman, C. M., & Stein, D. L. (2007). Local vs. global variables for spin glasses. In Spin Glasses (pp. 145-158). (Lecture Notes in Mathematics; Vol. 1900). Springer Verlag. https://doi.org/10.1007/978-3-540-40908-3_6