We study dynamic behavior of Potts model with invisible states near the first-order phase transition temperature. We focus on melting process starting from the perfect ordered state. This model is regarded as a standard model to analyze nature of phase transition. We can control the energy barrier between the ordered state and paramagnetic state without changing the symmetry which breaks at the transition point. We calculate time-dependency of the order parameter, density of invisible state, and internal energy. They show two-step relaxation behavior. We also consider the relation between the characteristic melting time and characteristic scale of the energy barrier by changing the number of invisible states. We find that characteristic melting time increases as the energy barrier enlarges in this model. Thus, this model is regarded as a fundamental model to analyze dynamic behavior near the first-order phase transition point.
Potts Models with Invisible States on General Bethe Lattices
为了使Potts模型的相变从连续相变变为一阶相变，需要在Potts模型中加入多少个所谓的不可见态，这一问题引起了人们的关注。在q=2的情况下，布拉格-威廉姆斯平均场方法需要4个这样的不可见态，而3-正则随机图形式主义需要17个。在这两种情况下，从二阶到一阶的行为引起的不可见状态的转换是通过一个等效的布卢姆-金刚砂-格里菲斯模型的三临界点确定的。在这里，我们调查广义Potts模型上的Bethe晶格z邻居。我们证明了在q=2的情况下，rc（z）=[4 z / 3（z-1）] [（z-1）/（z-2）]^z不可见态是等价的Blume-Emery-Griffiths三临界性的必要条件.当z=3时，恢复了3-正则随机图的结果，而无限z极限提供了布拉格-威廉姆斯平均场的结果。
Different models are proposed to understand magnetic phase transitions through the prism of competition between the energy and the entropy. One of such models is a $q$-state Potts model with invisible states. This model introduces $r$ invisible states such that if a spin lies in one of them, it does not interact with the rest states. We consider such a model using the mean field approximation on an annealed scale-free network where the probability of a randomly chosen vertex having a degree $k$ is governed by the power-law $P(k)\propto k^{-λ}$. Our results confirm that $q$, $r$ and $λ$ play a …
We present the exact solution of the 1D classical short-range Potts model with invisible states. Besides the $q$ states of the ordinary Potts model, this possesses $r$ additional states which contribute to the entropy, but not to the interaction energy. We determine the partition function, using the transfer-matrix method, in the general case of two ordering fields: $h_1$ acting on a visible state and $h_2$ on an invisible state. We analyse its zeros in the complex-temperature plane in the case that $h_1=0$. When ${\rm Im}\, h_2=0$ and $r\ge 0$, these zeros accumulate along a line that interse…
We reconsider the mean-field Potts model with $q$ interacting and $r$ non-interacting (invisible) states. The model was recently introduced to explain discrepancies between theoretical predictions and experimental observations of phase transitions in some systems where the $Z_q$-symmetry is spontaneously broken. We analyse the marginal dimensions of the model, i.e., the value of $r$ at which the order of the phase transition changes. In the $q=2$ case, we determine that value to be $r_c = 3.65(5)$; there is a second-order phase transition there when $r<r_c$ and a first-order one at $r>r_c$. We…
Phase transitions are ubiquitous phenomena, exemplified by the melting of ice and spontaneous magnetization of magnetic material. In general, a phase transition is associated with a symmetry breaking of a system; occurs due to the competition between coupling interaction and external fields such as thermal energy. If the phase transition occurs with no latent heat, the system experiences continuous transition, also known as second order phase transition. The ferromagnetic $q$-state Potts model with $r$ extra invisible states, introduced by Tamura, Tanaka, and Kawashima [Prog. Theor. Phys. 124,…
We present an exact renormalization group analysis of the Loschmidt amplitude of the quantum $N$-state Potts chain with random quench-disordered nearest neighbor bonds, under the extreme dynamical quantum quench. We prove that the phase transition of the Loschmidt rate function remains sharp in general. For typical bond distributions, the phase transition is found to be a linear-cusp, as in the pure model. For some special discrete bond distributions, however, the rate function exhibits logarithmic divergences. These singularities are due to the competition between the non-critical dynamical p…
We investigate the short-time critical dynamics of the Baxter-Wu (BW) and $n=3$ Turban (3TU) models to estimate their global persistence exponent $θ_{g}$. We conclude that this new dynamical exponent can be useful in detecting differences between the critical behavior of these models which are very difficult to obtain in usual simulations. In addition, we estimate again the dynamical exponents of the four-state Potts (FSP) model in order to compare them with results previously obtained for the BW and 3TU models and to decide between two sets of estimates presented in the current literature. We…
The $(2+1)$-dimensional $q=3$ Potts model was simulated with the exact diagonalization method. In the ordered phase, the elementary excitations (magnons) are attractive, forming a series of bound states in the low-energy spectrum. We investigate the low-lying spectrum through a dynamical susceptibility, which is readily tractable with the exact diagonalization method via the continued-fraction expansion. As a result, we estimate the series of (scaled) mass gaps, $m_{2,3,4}/m_1$ ($m_1$: single-magnon mass), in proximity to the transition point.
Ising's solution of a classical spin model famously demonstrated the absence of a positive-temperature phase transition in one-dimensional equilibrium systems with short-range interactions. No-go arguments established that the energy cost to insert domain walls in such systems is outweighed by entropy excess so that symmetry cannot be spontaneously broken. An archetypal way around the no-go theorems is to augment interaction energy by increasing the range of interaction. Here we introduce new ways around the no-go theorems by investigating entropy depletion instead. We implement this for the P…
We investigate the phase transitions of the $q$-state Brownian Potts model in two dimensions (2d) comprising Potts spins that diffuse like Brownian particles and interact ferromagnetically with other spins within a fixed distance. With extensive Monte Carlo simulations we find a continuous phase transition from a paramagnetic to a ferromagnetic phase even for $q>4$. This is in sharp contrast to the existence of a discontinuous phase transition in the equilibrium $q$-state Potts model in 2d with $q>4$. We present detailed numerical evidence for a continuous phase transition and argue that diffu…
Percolation Thresholds of the Fortuin-Kasteleyn Cluster for a Potts Gauge Glass Model on Complex Networks: Analytical Results on the Nishimori Line
这是由德Arcangelis等人指出的。[Europhys. Lett. 14（1991），515]，正确理解Edwards-Anderson模型中Fortuin-Kasteleyn团簇的渗透现象是重要的，因为由称为汉明距离或损伤的参数表征的动力学转变和渗透转变与自旋之间传播的信号的转变有关。我们分析了Fortuin-Kasteleyn集团的Potts规范玻璃模型，这是一个扩展的模型的爱德华-安德森模型，在随机图与任意度分布的逾渗阈值。结果显示在西森线上。我们还显示了无限范围模型的结果。
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Rudolf Peierls Centre for Theoretical Physics（鲁道夫·派尔斯理论物理中心）；Hertford College（赫特福德学院）
Using the corner-transfer matrix renormalization group approach, we revisit the three-state chiral Potts model on the square lattice, a model proposed in the eighties to describe commensurate-incommensurate transitions at surfaces, and with direct relevance to recent experiments on chains of Rydberg atoms. This model was suggested by Huse and Fisher to have a chiral transition in the vicinity of the Potts point, a possibility that turned out to be very difficult to definitely establish or refute numerically. Our results confirm that the transition changes character at a Lifshitz point that sep…
We show that dynamic quantum phase transitions (DQPT) in many situations involve renormalization group (RG) fixed points that are unphysical in the context of thermal phase transitions. In such cases, boundary conditions are shown to become relevant to the extent of even completely suppressing the bulk transitions. We establish these by performing exact RG analysis of the quantum Ising model on scale-invariant lattices of different dimensions, and by analyzing the zeros of the Loschmidt amplitude. Further corroboration of boundaries affecting the bulk transition comes from the three-state quan…
