Numerical determination of the order of phase transition of the two-dimensional Potts model with multispin interactions

1993 ◽  
Vol 26 (19) ◽  
pp. 4907-4910 ◽  
Author(s):  
Guo-Ming Zhang ◽  
Chuan-Zhang Yang
Keyword(s):  
Phase Transition ◽  
Potts Model ◽  
Two Dimensional ◽  
Numerical Determination ◽  
Order Of Phase Transition ◽  
Multispin Interactions

scholarly journals Geometrical four-point functions in the two-dimensional critical Q-state Potts model: the interchiral conformal bootstrap

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yifei He ◽  
Jesper Lykke Jacobsen ◽  
Hubert Saleur
Keyword(s):  
Potts Model ◽  
Correlation Functions ◽  
Liouville Theory ◽  
Analytical Determination ◽  
Conformal Weight ◽  
Two Dimensional ◽  
Conformal Blocks ◽  
Conformal Bootstrap ◽  
Point Correlation

Abstract Based on the spectrum identified in our earlier work [1], we numerically solve the bootstrap to determine four-point correlation functions of the geometrical connectivities in the Q-state Potts model. Crucial in our approach is the existence of “interchiral conformal blocks”, which arise from the degeneracy of fields with conformal weight hr,1, with r ∈ ℕ*, and are related to the underlying presence of the “interchiral algebra” introduced in [2]. We also find evidence for the existence of “renormalized” recursions, replacing those that follow from the degeneracy of the field $$ {\Phi}_{12}^D $$ Φ 12 D in Liouville theory, and obtain the first few such recursions in closed form. This hints at the possibility of the full analytical determination of correlation functions in this model.

Phase transition of a two-dimensional, multiplicatively coupledXY–Potts model

2009 ◽  
Vol 42 (22) ◽  
pp. 225001 ◽  
Author(s):  
Marcel Hellmann ◽  
Youjin Deng ◽  
Matthias Weiss ◽  
Dieter W Heermann
Keyword(s):  
Phase Transition ◽  
Potts Model ◽  
Two Dimensional

scholarly journals Numerical determination of the order of phase transitions in Ising systems with multispin interactions

1991 ◽  
Vol 43 (1) ◽  
pp. 1173-1175 ◽  
Author(s):  
Nestor Caticha ◽  
Jorge Chahine ◽  
J. R. Drugowich de Felriaacio
Keyword(s):  
Phase Transitions ◽  
Numerical Determination ◽  
Ising Systems ◽  
Multispin Interactions

Numerical determination of two-dimensional temperature fields in transpiration cooling

1984 ◽  
Vol 47 (6) ◽  
pp. 1459-1465
Author(s):  
A. V. Kurpatenkov ◽  
V. M. Polyaev ◽  
A. L. Sintsov
Keyword(s):  
Temperature Fields ◽  
Transpiration Cooling ◽  
Two Dimensional ◽  
Numerical Determination

Phase Transition Temperature of Ferroelectric Thin Film Evaluated by Four-State Potts Model

2005 ◽  
Vol 902 ◽  
Author(s):  
Wing Yee Winnie Chung ◽  
Veng Cheong Lo
Keyword(s):  
Thin Film ◽  
Phase Transition ◽  
Boundary Condition ◽  
Transition Temperature ◽  
Potts Model ◽  
Domain Walls ◽  
Ferroelectric Thin Film ◽  
Two Dimensional ◽  
Thermally Activated ◽  
Phase Transition Temperatures

AbstractAn epitaxial ferroelectric thin film can be modeled by a two-dimensional array of dipoles. The orientation of each dipole is assigned to one of the four possible states which are mutually perpendicular to each other. Consequently, the whole film can be divided into domains with both 90° and 180° domain walls. The dominant switching mechanism for individual dipole is implemented by a 90° rotation. Two different conditions have been considered. For the first one (model A), every dipole inside the film is allowed to rotate, provided that it is thermally activated. For the second (model B), only the dipole rotation is restricted to those at the domain walls. The phase transition temperatures under these two models have been evaluated. Furthermore, the effects of sample size and boundary condition are discussed.

scholarly journals Фазовые переходы в двумерной слабо разбавленной пятивершинной модели Поттса

2020 ◽  
Vol 62 (7) ◽  
pp. 1088
Author(s):  
А.К. Муртазаев ◽  
А.Б. Бабаев ◽  
Г.Я. Атаева
Keyword(s):  
Phase Transition ◽  
Order Phase Transition ◽  
Potts Model ◽  
Square Lattice ◽  
Study Phase ◽  
Two Dimensional ◽  
Nonmagnetic Impurities ◽  
First Order Phase Transition ◽  
First Order Phase ◽  
Binder Cumulants

Computer simulation was used to study phase transitions in the two-dimensional weakly diluted Potts model on a square lattice at q=5. Systems with linear dimensions L×L=N, L=10-120 are considered. Based on fourth-order Binder cumulants, it was shown that the introduction of nonmagnetic impurities into the spin system described by the two-dimensional Potts model with q=5 leads to a change in the first-order phase transition to the second-order phase transition.

ON THE DETERMINATION OF CRITICAL POINT IN HIGHER-ORDER VARIATIONAL CUMULANT EXPANSION

1996 ◽  
Vol 10 (12) ◽  
pp. 531-536 ◽  
Author(s):  
X.F. OU ◽  
J.T. OU ◽  
D.L. LIN
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
Phase Transitions ◽  
Ising Model ◽  
Critical Point ◽  
Spin System ◽  
Order Approximation ◽  
Two Dimensional ◽  
Cumulant Expansion

To the lowest order approximation, the method of variational cumulant expansion has been successful in the determination of the critical point of a spin system on the Ising model. In the second order calculation, unphysical phase transition arises. In this letter, we first analyze the origin of unphysical phase transitions in high-order variational cumulant expansion calculations. We then explain the basis on which a conjecture is proposed that to any order m of the variational cumulant expansion, the critical point is given by the bifurcation point of the free energy. The theory is finally verified numerically for the two-dimensional case.

IMPORTANCE-SAMPLING MONTE CARLO METHOD AND ENTROPY OF q-STATE POTTS MODEL

1992 ◽  
Vol 06 (18) ◽  
pp. 1121-1129
Author(s):  
HSING-MEI HUANG
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Importance Sampling ◽  
Potts Model ◽  
Continuous Phase ◽  
Entropy Function ◽  
Two Dimensional ◽  
Potts Models ◽  
Continuous Phase Transition

An importance-sampling Monte Carlo method is applied to the calculation of Γ(E), the number of states for a given energy E, and Γ(E, S), the number of states for given energy E and spin S, of antiferromagnetic two-dimensional q=2,3,4,5,6 Potts models. The entropy function is derived for various temperatures, and our results for the q=3 model show a continuous phase transition.

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