scholarly journals On four-point connectivities in the critical 2d Potts model

2019 ◽  
Vol 7 (4) ◽  
Author(s):  
Marco Picco ◽  
Sylvain Ribault ◽  
Raoul Santachiara
Keyword(s):  
Monte Carlo ◽  
Half Plane ◽  
Potts Model ◽  
Central Charge ◽  
Symmetry Algebra ◽  
Double Cover ◽  
Minimal Models ◽  
Virasoro Symmetry ◽  
Special Cases

We perform Monte-Carlo computations of four-point cluster connectivities in the critical 2d Potts model, for numbers of states Q\in (0,4)Q∈(0,4) that are not necessarily integer. We compare these connectivities to four-point functions in a CFT that interpolates between D-series minimal models. We find that 3 combinations of the 4 independent connectivities agree with CFT four-point functions, down to the 22 to 44 significant digits of our Monte-Carlo computations. However, we argue that the agreement is exact only in the special cases Q=0, 3, 4Q=0,3,4. We conjecture that the Potts model can be analytically continued to a double cover of the half-plane \{\Re c <13\}{ℜc<13}, where cc is the central charge of the Virasoro symmetry algebra.

scholarly journals INVESTIGATION OF THE 3-STATE, 2-D POTTS MODEL WITH ONE DEFECT LINE OF COUPLINGS BY DENSITY OF STATES MONTE CARLO METHOD

1992 ◽  
Vol 03 (06) ◽  
pp. 1195-1207 ◽  
Author(s):  
GÉZA ÓDOR
Keyword(s):  
Monte Carlo ◽  
Potts Model ◽  
Central Charge ◽  
Free Energy Density ◽  
Periodic Boundary Conditions ◽  
Lattice Systems ◽  
Monte Carlo Data ◽  
Defect Line ◽  
Point Correlation ◽  
Scaling Dimension

The critical 3-state two-dimensional Potts model with one line of defect couplings has been studied. Interpolating the coupling strength between the free and periodic boundary conditions renormalization group arguments suggest that the algebraic content should change discontinuously. Monte Carlo data on different sized and shaped lattice systems have been collected. Predictions for the surface-free energy density, the central charge and the magnetization two-point correlation scaling dimension are given.

scholarly journals Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$

2018 ◽  
Vol 5 (5) ◽  
Author(s):  
Victor Gorbenko ◽  
Slava Rychkov ◽  
Bernardo Zan
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Fixed Points ◽  
Potts Model ◽  
General Relation ◽  
Coupling Constants ◽  
Two Dimensional ◽  
Minimal Models ◽  
The Real ◽  
First Order

We study complex CFTs describing fixed points of the two-dimensional QQ-state Potts model with Q≻ 4Q>4. Their existence is closely related to the weak first-order phase transition and the "walking" renormalization group (RG) behavior present in the real Potts model at Q𕣒Q>4. The Potts model, apart from its own significance, serves as an ideal playground for testing this very general relation. Cluster formulation provides nonperturbative definition for a continuous range of parameter QQ, while Coulomb gas description and connection to minimal models provide some conformal data of the complex CFTs. We use one and two-loop conformal perturbation theory around complex CFTs to compute various properties of the real walking RG flow. These properties, such as drifting scaling dimensions, appear to be common features of the QFTs with walking RG flows, and can serve as a smoking gun for detecting walking in Monte Carlo simulations.The complex CFTs discussed in this work are perfectly well defined, and can in principle be seen in Monte Carlo simulations with complexified coupling constants. In particular, we predict a pair of S_5S5-symmetric complex CFTs with central charges c\approx 1.138 \pm 0.021 ic≈1.138±0.021i describing the fixed points of a 5-state dilute Potts model with complexified temperature and vacancy fugacity.

Simulation of Fabrication for Al2O3 Ceramic Tool Materials

2012 ◽  
Vol 500 ◽  
pp. 537-543 ◽  
Author(s):  
Bin Fang ◽  
Chuan Zhen Huang ◽  
Hong Tao Zhu ◽  
Chong Hai Xu
Keyword(s):  
Grain Size ◽  
Monte Carlo ◽  
Microstructure Evolution ◽  
Potts Model ◽  
Single Phase ◽  
Ceramic Tool ◽  
Tool Materials ◽  
Fabrication Parameters

The new Monte Carlo Potts model that couples with fabrication parameters and considers pores and additives has been developed in order to simulate the fabrication of single-phase ceramics tool materials. The microstructure evolution for single-phase Al2O3 ceramic tool materials is simulated with the different technology parameters. At the same time, the single-phase Al2O3 ceramic tool materials are fabricated with the corresponding technology parameters. The errors of grain size between the simulated and the experimental is 12.1 and18.2%.

THE ANNIHILATING IDEALS OF MINIMAL MODELS

1992 ◽  
Vol 07 (supp01a) ◽  
pp. 217-238 ◽  
Author(s):  
BORIS L. FEIGIN ◽  
TOMOKI NAKANISHI ◽  
HIROSI OOGURI
Keyword(s):  
Central Charge ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Finite Models ◽  
Conformal Field ◽  
Intimate Relation ◽  
Chiral Algebras

We describe several aspects of the annihilating ideals and reduced chiral algebras of conformal field theories, especially, minimal models of Wn algebras. The structure of the annihilating ideal and a vanishing condition is given. Using the annihilating ideal, the structure of quasi-finite models of the Virasoro (2,q) minimal models are studied, and their intimate relation to the Gordon identities are discussed. We also show the examples in which the reduced algebras of Wn and Wℓ algebras at the same central charge are isomorphic to each other.

Markov-Chain Monte Carlo and the Potts Model

2013 ◽  
pp. 275-286
Author(s):  
Benjamin A. Stickler ◽  
Ewald Schachinger
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Potts Model

scholarly journals On 2d CFTs that interpolate between minimal models

2019 ◽  
Vol 6 (6) ◽  
Author(s):  
Sylvain Ribault
Keyword(s):  
Correlation Functions ◽  
Central Charge ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Exactly Solvable ◽  
Structure Constants

We investigate exactly solvable two-dimensional conformal field theories that exist at generic values of the central charge, and that interpolate between A-series or D-series minimal models. When the central charge becomes rational, correlation functions of these CFTs may tend to correlation functions of minimal models, or diverge, or have finite limits which can be logarithmic. These results are based on analytic relations between four-point structure constants and residues of conformal blocks.

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