Universal properties of Ising clusters and droplets near criticality

2010/06/11 by Gesualdo Delfino, Jacopo Viti · 1 citation
Mathematics · Physics and Astronomy · #Amplitude #Condensed matter physics #Critical exponent #Criticality #Curie temperature #Ferromagnetism #Integrable system #Ising model #Materials science #Mathematical physics #Phase transition #Physics #Quantum mechanics #Random Matrices and Applications #Spins #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Universality (dynamical systems) #cond-mat.stat-mech #hep-th

paper · pdf · doi:10.1016/j.nuclphysb.2010.07.021

published as Nucl. Phys. B 840 (2010) 513 · 23 pages, 5 figures

arxiv created 2010/06/11 · openalex publication_date 2010/08/04 · arxiv updated 2014/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Clusters and droplets of positive spins in the two-dimensional Ising model percolate at the Curie temperature in absence of external field. The percolative exponents coincide with the magnetic ones for droplets but not for clusters. We use integrable field theory to determine amplitude ratios which characterize the approach to criticality within these two universality classes of percolative critical behavior.

Citations

• Spin-spin correlation functions for the two-dimensional Ising model: Exact theory in the scaling region
• Universal amplitude ratios of two-dimensional percolation from field theory
• Infinite conformal symmetry in two-dimensional quantum field theory
• Integrable aspects of the scaling q-state Potts models I: bound states and bootstrap closure
• Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models

Cited by

• On three-point connectivity in two-dimensional percolation