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Carlon, Enrico; Iglói, Ferenc; Selke, W.; Szalma, F.

doi:10.1023/a:1004542105635

Cited by 14 publications

(20 citation statements)

References 12 publications

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“…It is found to depend rather mildly on q. Note that the temperature dependent spread d w (T ) displays a maximum close to the critical point, as illustrated in Figure 3, similar to the behavior of W [3,8]. Its critical behavior, in the thermodynamic limit L → ∞, will be analyzed in the following subsection.…”

Section: Interfacial Propertiesmentioning

confidence: 68%

“…In the perfect 2D q-state Potts models the total interfacial adsorption W is known to vanish at zero and infinite temperature, with a maximum, for finite lattices, near the critical temperature T c . In the thermodynamic limit, W (T, L) diverges with characteristic critical exponents [3,8,13]. In the present article, we shall take a closer look at the interfacial adsorption by analyzing the corresponding profile, w l , as well.…”

Section: Interfacial Propertiesmentioning

confidence: 99%

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Interfacial adsorption in Potts models on the square lattice

et al. 2015

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Abstract. We study the effect of interfacial phenomena in two-dimensional perfect and random (or disordered) q-state Potts models with continuous phase transitions, using, mainly, Monte Carlo techniques. In particular, for the total interfacial adsorption, the critical behavior, including corrections to scaling, are analyzed. The role of randomness is scrutinized. Results are discussed applying scaling arguments and invoking findings for bulk critical properties. In all studied cases, i.e., q = 3, 4, and q = 8, the spread of the interfacial adsorption profiles is observed to increase linearly with the lattice size at the bulk transition point. PACS

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Section: Interfacial Propertiesmentioning

confidence: 68%

Section: Interfacial Propertiesmentioning

confidence: 99%

Interfacial adsorption in Potts models on the square lattice

et al. 2015

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“…We note that an alternative numerical method is to use Monte Carlo (MC) simulations on the classical model with L × M sites. As can be seen in an investigation of a related problem [27] the DMRG and the MC methods generally provide results with approximately the same accuracy using the same CPU times. with the analytical results in Eq.…”

Section: Numerical Studymentioning

confidence: 67%

Numerical study of the critical behavior of the Ashkin–Teller model at a line defect

Lajkó¹,

Iglói²

2011

J. Stat. Mech.

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We consider the Ashkin-Teller model on the square lattice, which is represented by two Ising models (σ and τ ) having a four-spin coupling of strength, ǫ, between them. We introduce an asymmetric defect line in the system along which the couplings in the σ Ising model are modified. In the Hamiltonian version of the model we study the scaling behavior of the critical magnetization at the defect, both for σ and for τ spins by density matrix renormalization. For ǫ > 0 we observe identical scaling for σ and τ spins, whereas for ǫ < 0 one model becomes locally ordered and the other locally disordered. This is different of the critical behavior of the uncoupled model (ǫ = 0) and is in contradiction with the results of recent field-theoretical calculations.

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“…In the large-q limit, at the critical point J c = 1, the ground state of the system is L-fold degenerate, having an energy E (0) 0 = −J(L−1). In a first-order perturbative treatment [12][13][14], corrections of the order of 1/ √ q are obtained through the solution of the following secular eigenvalue problem, hv α = ǫ α v α . Here h is a symmetric L × L matrix…”

Section: Discussionmentioning

confidence: 99%

“…(4.30) is supplemented by a surface-field term: The surface critical behavior of the quantum Potts model in the large-q limit has been studied in Refs. [12][13][14] and the results are summarized in Appendix B. In the large-q limit, corrections of the order of q −1/2 are taken into account and the distance from the critical point is defined as J c −J = θ/ √ q, where θ plays the role of a reduced temperature.…”

Section: E Solution In 2d For Large-q Valuesmentioning

confidence: 99%

Nonequilibrium phase transition in a driven Potts model with friction

2011

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We consider magnetic friction between two systems of q-state Potts spins which are moving along their boundaries with a relative constant velocity ν. Due to the interaction between the surface spins there is a permanent energy flow and the system is in a steady state, which is far from equilibrium. The problem is treated analytically in the limit ν=∞ (in one dimension, as well as in two dimensions for large-q values) and for v and q finite by Monte Carlo simulations in two dimensions. Exotic nonequilibrium phase transitions take place, the properties of which depend on the type of phase transition in equilibrium. When this latter transition is of first order, a sequence of second- and first-order nonequilibrium transitions can be observed when the interaction is varied.

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Untitled

Cited by 14 publications

References 12 publications

Interfacial adsorption in Potts models on the square lattice

Interfacial adsorption in Potts models on the square lattice

Numerical study of the critical behavior of the Ashkin–Teller model at a line defect

Nonequilibrium phase transition in a driven Potts model with friction

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