An Energy Curve Family of a Semi-Infinite Lattice and the Transition Point in the Potts Model

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概要

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• An energy curve family for a semi-infinite square lattice (l × ∞) of the q-state Potts model with periodic boundary conditions has an l-independent common fixed point, which gives the exact critical values of the coupling parameter K = J/kT and the internal energy E (K), as a natural consequence of the self-dual property of the model.An energy curve intersection procedure (ECIP) is proposed to find the critical properties of the Potts model through numerical investigation of the transfer matrix.The ECIP shows that the lattices (l × ∞) for two different small values of l can reproduce the transition temperature and the critical internal energy of the bulk lattice (∞ × ∞) without use of the duality argument. As an applicable example of the ECIP, a semi-infinite simple cubic lattice (l × m × ∞) of the Potts model is preliminarily studied to obtain approximate critical quantities of the layer lattice (l × ∞ × ∞).A brief comment on the specific heat exponent μ estimated using the ECIP is added.

• 理論物理学刊行会の論文
• 2000-06-25

著者

• Katsumori Hiroshi

  Chubu University

• Katsumori H

  Chubu University

• OHYA Shingo

  Nagoya Bunri University

• Ohya S

  Nagoya Bunri University

• Ohya Shingo

  Nagoya Bunri College

• KATSUMORI Hiroshi

  Department of Applied Physics, Chubu Institute of Technology

関連論文

• Finite Size Effects and Pseudocritical Behavior. I : Ising Spin and Lattice Gauge Models
• An Energy Curve Family of a Semi-Infinite Lattice and the Transition Point in the Potts Model
• Specific Heat of Three-Dimensional Ising Model
• An Energy Curve Family and the Transition Point of the Simple Cubic Layer Potts Model
• Successive Screw Approximation in Ising Lattice Gauge Theory
• Three-Dimensional Anisotropic Ising Lattice
• Finite Size Effects and Pseudocritical Behavior. II : Potts Spin Model
• A Phenomenological Mass Formula for Leptons and Quarks : Particles and Fields

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