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Chang, Shu Chiuan; Salas, José Valero; Shrock, Robert

doi:10.1023/a:1015165926201

Cited by 39 publications

(79 citation statements)

References 8 publications

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“…13-16) are very similar to those obtained in Ref. [39] for the Potts model with fully free boundary conditions. On the other hand, we have already seen that the B L with free cyclic boundary conditions are very different.…”

Section: Fixed Cyclic Boundary Conditionssupporting

confidence: 86%

“…The results are displayed in Figure 14. We have compared these curves with those obtained for a square-lattice strip with free boundary conditions [39]. We find that they agree almost perfectly in the region Re x ≥ −1.…”

Section: Three-state Potts Model (P = 6)mentioning

confidence: 69%

“…As a matter of fact, these branches extend to infinity (i.e., they are unbounded 14 ), in sharp contrast with the bounded limiting curves obtained using free longitudinal boundary conditions [39,40]. It is important to remark that this phenomenon also holds in the limit p → ∞, as shown in Figure 8.…”

Section: Asymptotic Behavior For |X| → ∞mentioning

confidence: 83%

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Complex-temperature phase diagram of Potts and RSOS models

2006

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We study the phase diagram of Q-state Potts models, for Q = 4 cos 2 (π/p) a Beraha number (p > 2 integer), in the complex-temperature plane. The models are defined on L × N strips of the square or triangular lattice, with boundary conditions on the Potts spins that are periodic in the longitudinal (N ) direction and free or fixed in the transverse (L) direction. The relevant partition functions can then be computed as sums over partition functions of an A p−1 type RSOS model, thus making contact with the theory of quantum groups. We compute the accumulation sets, as N → ∞, of partition function zeros for p = 4, 5, 6, ∞ and L = 2, 3, 4 and study selected features for p > 6 and/or L > 4. This information enables us to formulate several conjectures about the thermodynamic limit, L → ∞, of these accumulation sets. The resulting phase diagrams are quite different from those of the generic case (irrational p). For free transverse boundary conditions, the partition function zeros are found to be dense in large parts of the complex plane, even for the Ising model (p = 4). We show how this feature is modified by taking fixed transverse boundary conditions.

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Section: Fixed Cyclic Boundary Conditionssupporting

confidence: 86%

Section: Three-state Potts Model (P = 6)mentioning

confidence: 69%

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Complex-temperature phase diagram of Potts and RSOS models

2006

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“…q − 1, the full transfer matrix in Eq. (2.2) has a triangular block (submatrix) form, and the block corresponding to a d-color assignment has a diagonal block form withc 27) where [ν] denotes the integral part of ν. Here K is the diagonal matrix with diagonal element w ℓ , where ℓ is the number of vertices in the q = 1 state for the corresponding basis element.…”

Section: A Basic Methods Of Analysis and Structure For Cyclic And Möbmentioning

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

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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.

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“…We also apply this procedure for larger strip widths, using the exact calculation of f for sq, 4 F and sq, 5 F in Ref. [35] (see also [37]). The resulting values of k are plotted as functions of p in Fig.…”

Section: F 4f 5fmentioning

confidence: 99%

Exact results for average cluster numbers in bond percolation on lattice strips

Chang¹,

Shrock²

2004

Phys. Rev. E

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We present exact calculations of the average number of connected clusters per site, k , as a function of bond occupation probability p, for the bond percolation problem on infinite-length strips of finite width Ly, of the square, triangular, honeycomb, and kagomé lattices Λ with various boundary conditions. These are used to study the approach of k , for a given p and Λ, to its value on the two-dimensional lattice as the strip width increases. We investigate the singularities of k in the complex p plane and their influence on the radii of convergence of the Taylor series expansions of k about p = 0 and p = 1.

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Cited by 39 publications

References 8 publications

Complex-temperature phase diagram of Potts and RSOS models

Complex-temperature phase diagram of Potts and RSOS models

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

Exact results for average cluster numbers in bond percolation on lattice strips

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