Structure of the partition function and transfer matrices for the potts model in a magnetic field on lattice strips

Shu Chiuan Chang, Robert Shrock

研究成果: Article同行評審

8 引文 斯高帕斯(Scopus)

摘要

We determine the general structure of the partition function of the q-state Potts model in an external magnetic field, Z(G,q,v,w) for arbitrary q, temperature variable v, and magnetic field variable w, on cyclic, Möbius, and free strip graphs G of the square (sq), triangular (tri), and honeycomb (hc) lattices with width Ly and arbitrarily great length Lx. For the cyclic case we prove that the partition function has the form, where Λ denotes the lattice type, c̃(d) are specified polynomials of degree d in q, TZ,Λ,Ly,d is the corresponding transfer matrix, and m=Lx (Lx/2) for Λ=sq,tri (hc), respectively. An analogous formula is given for Möbius strips, while only TZ,Λ,Ly,d=0 appears for free strips. We exhibit a method for calculating TZ,Λ,Ly,d for arbitrary Ly and give illustrative examples. Explicit results for arbitrary Ly are presented for TZ,Λ,Ly,d with d=Ly and d=Ly-1. We find very simple formulas for the determinant det(TZ,Λ,Ly,d). We also give results for self-dual cyclic strips of the square lattice.

原文English
頁(從 - 到)667-699
頁數33
期刊Journal of Statistical Physics
137
發行號4
DOIs
出版狀態Published - 2009 11月

All Science Journal Classification (ASJC) codes

  • 統計與非線性物理學
  • 數學物理學

指紋

深入研究「Structure of the partition function and transfer matrices for the potts model in a magnetic field on lattice strips」主題。共同形成了獨特的指紋。

引用此