Three-dimensional Three-state Potts Model Research Articles

Persistent Homology Analysis for Dense QCD Effective Model with Heavy Quarks

The isospin chemical potential region is known as the sign-problem-free region of quantum chromodynamics (QCD). In this paper, we introduce the isospin chemical potential to the three-dimensional three-state Potts model to mimic dense QCD; e.g., the QCD effective model with heavy quarks at finite density. We call it the QCD-like Potts model. The QCD-like Potts model does not have a sign problem, but we expect it to share some properties with QCD. Since we can obtain the non-approximated Potts spin configuration at finite isospin chemical potential, where the simple Metropolis algorithm can work, we perform the persistent homology analysis toward exploring the dense spatial structure of QCD. We show that the averaged birth-death ratio has the same information with the Polyakov loop, but the maximum birth-death ratio has additional information near the phase transition where the birth-death ratio means the ratio of the creation time of a hole and its vanishing time based on the persistent homology.

Information theoretical view of QCD effective model with heavy quarks

To understand the phase transition phenomena, information theoretical approaches can pick up some important properties of the phenomena based on the probability distribution. In this paper, we show information theoretical aspects of the three-dimensional three-state Potts model with the external field which is corresponded to the QCD effective model with heavy quarks. The transfer mutual information which represents the information flow of two spin variables is numerically estimated based on the Markov-chain Monte Carlo method. The transfer mutual information has the peak near the confinement-deconfinement transition, and it may be used to detect the precursors of the transition. Since the transfer mutual information still has the peak even if the Polyakov-loop changes continuously and smoothly, we may pick up some aspects of the confinement-deconfinement nature from the information flow properties. Particularly, the transfer mutual information shows the significantly different behavior below and above the Roberge-Weiss endpoint existed in the pure imaginary chemical potential region, which may indicate the system change by the confinement-deconfinement transition.

Locating fixed points in the phase plane.

The critical point is a fixed point in finite-size scaling. To quantify the behavior of such a fixed point, we define, at a given temperature and scaling exponent ratio, the width of scaled observables for different sizes. The minimum of the width reveals the position of the fixed point, its corresponding phase transition temperature, and scaling exponent ratio. The value of this ratio tells the nature of the fixed point, which can be a critical point, a point of the first-order phase transition line, or a point of the crossover region. To demonstrate the effectiveness of this method, we apply it to three typical samples produced by the three-dimensional three-state Potts model. Results show the method to be more precise and effective than conventional methods. Finally, we discuss a possible application at the Beam Energy Scan program of the Relativistic Heavy Ion Collider.

Finite-size behaviour of generalized susceptibilities in the whole phase plane of the Potts model**Supported by Fund Project of National Natural Science Foundation of China (11647093, 11405088, 11521064), Fund Project of Sichuan Provincial Department of Education (16ZB0339), Fund Project of Chengdu Technological University (2016RC004) and the Major State Basic Research Development Program of China (2014CB845402)

We study the sign distribution of generalized magnetic susceptibilities in the temperature-external magnetic field plane using the three-dimensional three-state Potts model. We find that the sign of odd-order susceptibility is opposite in the symmetric (disorder) and broken (order) phases, but that of the even-order one remains positive when it is far away from the phase boundary. When the critical point is approached from the crossover side, negative fourth-order magnetic susceptibility is observable. It is also demonstrated that non-monotonic behavior occurs in the temperature dependence of the generalized susceptibilities of the energy. The finite-size scaling behavior of the specific heat in this model is mainly controlled by the critical exponent of the magnetic susceptibility in the three-dimensional Ising universality class.

Corrections to scaling in the dynamic approach to the phase transition with quenched disorder

With dynamic Monte Carlo simulations, we investigate the continuous phase transition in the three-dimensional three-state random-bond Potts model. We propose a useful technique to deal with the strong corrections to the dynamic scaling form. The critical point, static exponents β and ν, and dynamic exponent z are accurately determined. Particularly, the results support that the exponent ν satisfies the lower bound .

Positive specific-heat critical exponent of a three-dimensional three-state random-bond Potts model

Whereas the stability of a pure critical system is determined by the sign of its specific-heat critical exponent α according to Harrisʼ criterion, whether a d-dimensional dirty system should satisfy ν⩾2/d and α<0 or not has been a controversial issue for several decades, where ν is its correlation-length critical exponent. Here, contrary to recent analytical and numerical results, we find for the three-dimensional three-state random-bond Potts model whose pure version exhibits a first-order phase transition a random fixed point whose ν<2/d and α>0 using a finite-time scaling combining with extended dynamic Monte Carlo renormalization-group method. This suggests further studies are still needed to clarify the issue in three-dimensional systems.

Dynamic Monte Carlo simulations of the three-dimensional random-bond Potts model

The effect of random bonds on the phase transitions of the three-dimensional three-state Potts model is investigated with extensive dynamic Monte Carlo simulations. In the weakly disordered regime, the phase diagram is obtained with a recently suggested nonequilibrium reweighting method. The tricritical point separating the first- and second-order transitions is determined, and the critical exponents of the continuous phase transition induced by quenched randomness are estimated.

Critical behavior in the site-diluted three-dimensional three-state Potts model

We have studied numerically the effect of quenched site dilution on a first order phase transition in three dimensions. We have simulated the site diluted three states Potts model studying in detail the second order region of its phase diagram. We have found that the $\nu$ exponent is compatible with the one of the three dimensional diluted Ising model whereas the $\eta$ exponent is definitely different.

The three-state antiferromagnetic Potts model: Scaling laws

We present the results of a Monte Carlo study of the three-dimensional anti-ferromagnetic three-state Potts model. We computed the correlation length, the magnetic susceptibility and the specific heat for various coupling parameters in the high temperature phase of the model. From the scaling behaviour of these quantities we determine estimates for the critical temperature and critical exponents.

Interfacial adsorption phenomena of the three-dimensional three-state Potts model

The authors study the interfacial adsorption phenomena of the three-state ferromagnetic Potts model on the simple cubic lattice by the Monte Carlo method. Finite-size scaling analyses of the net adsorption yield evidence of the phase transition being of first order and kBTC/J=1.8166(2).

The Phase Transition in the Three-State Potts Model: An Analytical Analysis11The project supported by the Science Foundation of Henan Education Committee and Henan Science Committee.

We investigate the phase transition of the three-state Potts model in an analytical approach—the generalized cumulant expansion with the effective mean field hypothesis. We find a first order phase transition in the three-dimensional three-state Potts model with ferromagnetic nearest neighbor coupling. For the model with antiferromagnetic next-to-nearest neighbor coupling, we find a first order transition when the relative strength of the -coupling is fixed to . The critical values given by this method are also in agreement with the recent high statistics Monte Carlo results.

Microcanonical simulation of first-order phase transitions in finite volumes

Microcanonical studies of first-order phase transitions provide essentially the same information as canonical ensemble calculations, and offer no significant advantage over the more common canonical approach. Interpretation of the S-shaped energy-temperature curve that signals a first-order transition as a “van der Waals” curve whose extrema denote “limits of metastability” and bracket an accesible “unstable phase” is unjustified; a simple model of finite-volume effects reproduces such S-shaped curves with good accuracy, as illustrated by the three-dimensional three-state Potts model.

Potts models: Density of states and mass gap from Monte Carlo calculations.

Monte Carlo simulations are performed for first-order phase-transition models. The three-dimensional three-state Potts model has a weak first-order transition. For this model we calculate the density of states on ${\mathit{L}}^{3}$ block lattices (L up to size 36) and obtain high-precision estimates for the leading partition-function zeros. The finite-size-scaling analysis of the first zero exhibits the expected convergence of the critical exponent \ensuremath{\nu} toward 1/D for large L; in particular, we find \ensuremath{\nu}=2.955(26) from our two largest lattices. Analysis of our specific-heat ${\mathit{C}}_{\mathit{v}}$ data yields l=0.080 31(26) for the latent heat. Along another line of approach, we calculate the mass gap m=1/\ensuremath{\xi} (\ensuremath{\xi} is the correlation length) for cylindrical ${\mathit{L}}^{2}$${\mathit{L}}_{\mathit{z}}$ lattices (L up to 24 and ${\mathit{L}}_{\mathit{z}}$=256). The finite size-scaling analysis of these results is also consistent with the convergence of \ensuremath{\nu} toward 1/D, but that the limiting value is 1/D is not yet conclusively established. Some theoretical arguments favor \ensuremath{\nu}\ensuremath{\rightarrow}0 in case of a first-order transition in a cylindrical ${\mathit{L}}^{\mathit{D}\mathrm{\ensuremath{-}}1}$\ensuremath{\infty} geometry. Therefore, we also applied our approach to the 2D ten-state Potts model, which is known to have a strong first-order transition. In this case we find unambiguous evidence in favor of 1/D as the limiting value.

Domain walls, surface tension and wetting in the three-dimensional three-state Potts model

We study the thermodynamic properties of interfaces between differently ordered domains in the three-dimensional three-state Potts model. We perform simulations on lattices with cylindric geometry, using parallel and rotated fixed boundary conditions. Systematic control over finite-size effects and the number of interfaces is achieved. Global and local characterization of the interfacial structure is given and substantial evidence for complete wetting is presented.

Finite-size effects and phase transition in the three-dimensional three-state Potts model

The three-state Potts model in three dimensions is studied by Monte Carlo and finite-size scaling techniques. Using a histogram method recently proposed by Ferrenberg and Swendsen, the finite-size dependence for the maximum of the specific heat is found to scale with the volume of the system, indicating that the phase transition is of first order. The value of the latent heat per spin and the correlation length at the transition are estimated.

Deconfinement in QCD: An analysis of the phase transition

I discuss the Ape group results concerning the deconfining transition in finite temperature lattice quantum chromodynamics. I discuss in detail our evidence for a very large correlation length at the critical point, suggestive of a weak first order or second order transition. I discuss methods and observable quantities (source, smearing, blocking), the details of the numerical simulations (finite separation mass estimators, fits), measurements of the correlation length in the glue ball channels, the three-dimensional three-state Potts model.

A study of the correlation length near a first-order phase transition: The three-dimensional three-state Potts model

A high statistics study of the 3-d three-state Potts model on lattices of size L 3, with L ranging from 12 to 48, confirms the first-order nature of the Z(3) symmetry breaking phase transition in this model. We investigate the behaviour of spin-spin correlations in the critical region, comment on various methods to extract the correlation lengths and point out the resulting ambiguities on finite lattices. Our results indicate a finite correlation length at β c. However, a careful analysis of the correlation functions is necessary to disentangle the inverse mass gap from the tunnelling correlation length which we found to diverge as L at β c although the transition is clearly first order.

Absence of Z 3 criticality in a three-dimensional Potts model with extended couplings

The order-disorder phase transition has been reported to be of second order in the three-dimensional three-state Potts model with ferromagnetic nearest-neighbor ( J 1) and antiferromagnetic next-to-nearest-neighbor ( J 2) couplings. This contradicts the conventional picture in which Z 3 criticality does not exist in three dimensions and has been proposed as a concrete example of the “fluctuation-induced second-order phase transition” of Fucito and Parisi. Monte Carlo calculations on 32 3 and 64 3 lattices (for J 2 J 1=−0.1 and −0.2 ) demonstrate, however, that this phase transition is of first order, in keeping with conventional expectations.

Quenched dilution tricritical point in the q=3, d=4 Potts model

Abstract The effects of quenched site and bond dilution in the three-dimensional three-state Potts model are studied via the microcanonical simulation. In both systems we observe the following picture as quenched dilutions are added: the line of first order phase transitions originating with the pure system terminates at a tricritical point, and the resulting second order phase transition line has a continuously decreasing specific heat exponent for increasing dilutions.

The excess optical birefringence and phase transition in sodium nitrate

The temperature evolution of the birefringence in sodium nitrate shows a phase transition at 552 K which is continuous within experimental resolution (0.1 K). The excess birefringence is found to relate to the spontaneous strain via a temperature-independent elasto-optic coefficient. This behaviour is discussed microscopically in terms of structural and electronic contributions and is related to the order parameter by symmetry arguments. The critical exponent beta is then found to take the non-classical value of 0.22+or-0.01. This together with recent specific heat results indicate that the three-dimensional three-state Potts model provides a possible description of this phase transition provided the effects of defects are taken into account. Residual excess birefringence is observed above Tc. A model involving 'ordered' and 'anti-ordered' configurations is proposed and orientational fluctuations in the anti-ordered configuration as well as sodium sublattice melting are proposed to account for this phenomenon.