Continuum limits and exact finite-size-scaling functions for one-dimensional \(O(N)\)-invariant spin models

DOI10.1007/BF02199114zbMath0937.82006arXivhep-lat/9509021MaRDI QIDQ1285284

Alan D. Sokal, Attilio Cucchieri, Tereza Mendes, Andrea Pelissetto

Publication date: 6 June 2000

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-lat/9509021

zbMATH Keywords

continuum limitone-dimensionalfinite-size scalinghyperspherical harmonics\(\sigma\)-modeluniversality classes\(N\)-vector model\(RP^{N-1}\) modelmixed isovector/isotensor model

Mathematics Subject Classification ID

Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Finite-dimensional groups and algebras motivated by physics and their representations (81R05)

Related Items (4)

Modeling finite-volume effects and chiral symmetry breaking in two-flavor QCD thermodynamics ⋮ Pathologies of the large-\(N\) limit for \(\mathbb{RP}^{N-1}\), \(\mathbb{CP}^{N-1}\), \(\mathbb{QP}^{N-1}\) and mixed isovector/isotensor \(\sigma\)-models ⋮ Critical structure factors of bilinear fields in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">O</mml:mi><mml:mn /><mml:mo>(</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo><mml:mn /></mml:math>vector models ⋮ Pseudo-character expansions for \(U(N)\)-invariant spin models on \(CP^{N-1}\)

Cites Work

• The Monte Carlo method for the study of phase transitions: A review of some recent progress
• The continuum limit of one-dimensional non-linear models
• Theta functions, modular invariance, and strings
• Nonsymmetric first-order transitions: finite-size scaling and tests for infinite-range models.
• Statistical Field Theory
• Spherical Harmonics
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