On the slow decay of \(O(2)\) correlations in the absence of topological excitations: Remark on the Patrascioiu-Seiler model

DOI10.1007/BF02186846zbMath0838.60096MaRDI QIDQ1906414

Michael Aizenman

Publication date: 19 March 1996

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

zbMATH Keywords

topological chargesFortuin-Kasteleyn representationdecay of correlationsKosterlitz-Thouless transitioncontinuous symmetry

Mathematics Subject Classification ID

Other physical applications of random processes (60K40) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10)

Related Items (11)

Rarity of extremal edges in random surfaces and other theoretical applications of cluster algorithms ⋮ Continuous versus discrete spins in the hyperbolic plane ⋮ Topological lattice actions ⋮ Lectures on the Spin and Loop O(n) Models ⋮ Delocalization of two-dimensional random surfaces with hard-core constraints ⋮ Dobrushin interfaces via reflection positivity ⋮ Percolation phenomena in low and high density systems ⋮ 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 ⋮ Random cluster models on the triangular lattice ⋮ A model with simultaneous first and second order phase transitions ⋮ A slow decay of a connectivity function in a broad class of SOS models.

Cites Work

• Geometric aspects of quantum spin states
• Phase structure of two-dimensional spin models and percolation
• Discontinuity of the magnetization in one-dimensional \(1/| x-y| ^ 2\) Ising and Potts models.

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