The partition function zeros in the one-dimensional q-state Potts model

Glumac, Zvonko; Uzelac, Katarina

doi:10.1088/0305-4470/27/23/014

Cited by 36 publications

(66 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These values satisfy the scaling law α e + 2β e + γ e = 2. Table V into each other in one dimension [81]. In two dimensions it is known that σ e = − for the Fisher edge singularity, we have α e = 7 6 , β e = − 1 6 , and γ e = 7 6 , which are not far from the values of the exponents estimated by series expansions.…”

Section: /Nsmentioning

confidence: 65%

“…The study of the Yang-Lee edge singularity has been extended to the classical n-vector model [76], the quantum Heisenberg model [76], the spherical model [77], the quantum one-dimensional transverse Ising model [78], the hierarchical model [79], the one-dimensional Potts model [80,81], branched polymers [82], fluid models with repulsive-core interactions [83,84], etc. Dhar [85] calculated the edge critical exponent σ e in two dimensions by solving a particular model of three-dimensional directed animals and mapping the solution to the hard hexagon model.…”

Section: /Nsmentioning

confidence: 99%

See 1 more Smart Citation

Partition function zeros of the Q-state Potts model on the simple-cubic lattice

Kim

2002

Nuclear Physics B

View full text Add to dashboard Cite

The Q-state Potts model on the simple-cubic lattice is studied using the zeros of the exact partition function on a finite lattice. The critical behavior of the model in the ferromagnetic and antiferromagnetic phases is discussed based on the distribution of the zeros in the complex temperature plane. The characteristic exponents at complex-temperature singularities, which coexist with the physical critical points in the complex temperature plane for no magnetic field (H q = 0), are estimated using the low-temperature series expansion. We also study the partition function zeros of the Potts model for nonzero magnetic field. For H q > 0 the physical critical points disappear and the Fisher edge singularities appear in the complex temperature plane. The characteristic exponents at the Fisher edge singularities are calculated using the high-field, low-temperature series expansion. It seems that the Fisher edge singularity is related to the Yang-Lee edge singularity which appears in the complex magnetic-field plane for T > T c .

show abstract

Section: /Nsmentioning

confidence: 65%

Section: /Nsmentioning

confidence: 99%

Partition function zeros of the Q-state Potts model on the simple-cubic lattice

Kim

2002

Nuclear Physics B

View full text Add to dashboard Cite

show abstract

“…The results for eigenvalues agree. (The actual transfer matrices themselves are basis-dependent, and the basis used in [43] was different from ours, so the matrices are different, but the only part of the transfer matrices that enters into the partition function is the (powers of the) eigenvalues. )…”

Section: General Results For Cyclic Self-dual Square-lattice Stripsmentioning

confidence: 99%

Structure of the Partition Function and Transfer Matrices for the Potts Model in a Magnetic Field on Lattice Strips

Chang

Shrock

2009

J Stat Phys

View full text Add to dashboard Cite

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 Z(Λ, Ly ×Lx, q, v, w) = P Ly, where Λ denotes the lattice type,c (d) are specified polynomials of degree d in q, T Z,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 T Z,Λ,Ly ,d=0 appears for free strips. We exhibit a method for calculating T Z,Λ,Ly ,d for arbitrary Ly and give illustrative examples. Explicit results for arbitrary Ly are presented for T Z,Λ,Ly ,d with d = Ly and d = Ly − 1. We find very simple formulas for the determinant det(T Z,Λ,Ly,d ). We also give results for self-dual cyclic strips of the square lattice.

show abstract

“…For the one-dimensional Potts model in an external field the eigenvalues of the transfer matrix were found by Glumac and Uzelac [30]. The eigenvalues are λ ± = (A ± iB)/2, where…”

Section: Partition Functionmentioning

confidence: 97%

“…Mittag and Stephen [29] studied the Yang-Lee zeros of the three-state Potts ferromagnet in one dimension. Glumac and Uzelac [30] found the eigenvalues of the transfer matrix of the one-dimensional Potts model for general Q.…”

Section: Introductionmentioning

confidence: 99%