正方晶格上自旋为1的经典Blume-Capel模型在1+1时空维中表现出有限温度的相变，由三临界Ising CFT描述。这种相变可以用经典的蒙特卡罗模拟来实现，通过复制技巧计算，可以用来研究被分成两个圆柱体的环面的经典Rényi熵的形状依赖性。从第二Rényi熵，我们计算几何互信息（GMI）介绍了斯蒂芬等。[Phys. Rev. Lett. 112，127204（2014）]，并使用它来提取三临界点附近的中心荷值的数值估计。通过与已知的CFT结果$c=7/10$的比较，我们展示了如何使用这种类型的GMI计算来估计相图中三临界点的位置。
英文摘要：
The spin-1 classical Blume-Capel model on a square lattice is known to exhibit a finite-temperature phase transition described by the tricritical Ising CFT in 1+1 space-time dimensions. This phase transition can be accessed with classical Monte Carlo simulations, which, via a replica-trick calculation, can be used to study the shape-dependence of the classical Rényi entropies for a torus divided into two cylinders. From the second Rényi entropy, we calculate the Geometrical Mutual Information (GMI) introduced by Stéphan et. al. [Phys. Rev. Lett. 112, 127204 (2014)] and use it to extract a numerical estimate for the value of the central charge near the tricritical point. By comparing to the known CFT result, $c=7/10$, we demonstrate how this type of GMI calculation can be used to estimate the position of the tricritical point in the phase diagram.
Transverse field effect on thermodynamic properties of the spin-3/2 Blume-Capel model on rectangular lattice in which the interactions in perpendicular directions differ in signs is studied within the mean field approximation. Phase diagrams in the (transverse field, temperature) plane are constructed for various values of single-ion anisotropy.
We study the zero temperature steady state of the random field Blume Capel model with spin-flip Glauber dynamics on a random regular graph. The magnetization m as a function of the external field H is observed to have double hysteresis loops with a return point memory. We also solve the model on a Bethe lattice in the approximation that the spin relaxation dynamics is abelian and find good agreement between simulations on random regular graphs and Bethe lattice calculations for negative values of H.
The trilayered Blume-Capel ($S=1$) magnet with nearest neighbour intralayer ferromagnetic and nearest neighbour interlayer antiferromagnetic interaction is studied by Monte Carlo simulation. Depending on the relative interaction strength and the value of anisotropy the critical temperature (where all the sublattice magnetisations and consequently the total magnetisation vanishes) and the compensation temperature (where the total magnetisation vanishes for a special combination of nonzero sublattice magnetisations) are estimated. The comprehensive phase diagrams with lines of critical temperatu…
Expansions through the 24th order at high-temperature and up to 11th order at low-temperature are derived for the main observables of the Blume-Capel model on bipartite lattices (sq, sc and bcc) in 2d and 3d with various values of the spin and in presence of a magnetic field. All expansion coefficients are computed exactly as functions of the crystal and magnetic fields. Several critical properties of the model are analyzed in the two most studied cases of spin S=1 and S=3/2.
We compute two- and three-point functions at criticality for the three-dimensional Ising universality class. To this end we simulate the improved Blume-Capel model at the critical temperature on lattices of a linear size up to $L=1600$. As check also simulations of the spin-1/2 Ising model are performed. We find $f_{σσε} = 1.051(1)$ and $f_{εεε} =1.533(5)$ for operator product expansion coefficients. These results are consistent with but less precise than those recently obtained by using the bootstrap method. An important ingredient in our simulations is a variance reduced estimator of $N$-poi…
Using the approach based on the Bogoliubov inequality for free energy, we have studied the magnetic properties of the spin-3/2 Blume-Capel quantum model in the presence of the random transverse single-ion anisotropy (RTSIA). By analyzis of the phase diagrams in $τ\times φ_{x} $, $m \times φ_{x}$ and $m \times τ$ plans, we have obtained information about how the presence of anisotropy affects the properties of the system. We have shown that the RTSIA is responsible for changing the topology of the phase diagrams, compared to the pure model, leading to the appearance tricritical point (TCP).
We broaden the study of the statistical physics of the spin-$S$ Blume-Capel model with ferromagnetic mean-field interactions $J$ in competition with short-range antiferromagnetic interactions $K$ in a linear chain in the thermodynamic limit. This work describes the critical behavior of the model when the $S$ takes a half integer and an integer value. In both cases the phase diagrams exhibit new ferromagnetic phases (for certain values of $K$) enclosed by branches emerging from the first-order frontiers of the pure ferromagnetic model. For finite temperatures the complex topologies were obtaine…
We report on large-scale Wang-Landau Monte Carlo simulations of the critical behavior of two spin models in two- (2d) and three-dimensions (3d), namely the 2d random-bond Ising model and the pure 3d Blume-Capel model at zero crystal-field coupling. The numerical data we obtain and the relevant finite-size scaling analysis provide clear answers regarding the universality aspects of both models. In particular, for the random-bond case of the 2d Ising model the theoretically predicted strong universality's hypothesis is verified, whereas for the second-order regime of the Blume-Capel model, the e…
We study purely dissipative relaxational dynamics in the three-dimensional Ising universality class. To this end, we simulate the improved Blume-Capel model on the simple cubic lattice by using local algorithms. We perform a finite size scaling analysis of the integrated autocorrelation time of the magnetic susceptibility in equilibrium at the critical point. We obtain $z=2.0245(15)$ for the dynamic critical exponent. As a complement, fully magnetized configurations are suddenly quenched to the critical temperature, giving consistent results for the dynamic critical exponent. Furthermore, our …
The spin-3/2 Blume-Capel model on a rectangular lattice with the ferromagnetic bilinear short-range interaction $K^{\rm F}=K(1+x)$ in one direction and the anti-ferromagnetic one $K^{\rm AF}=K(-1+x)$ in the perpendicular direction under a longitudinal magnetic field and in the presence of a single-ion anisotropy is investigated within the mean field approximation. The quantity $x$ characterizes coupling between the interactions in the perpendicular directions and its absolute value does not exceed unity. Basing on the study of temperature dependencies of sublattice magnetizations the phase dia…
We present an extensive Monte Carlo investigation of the metastable lifetime through the reversal of the magnetization of spin-$s$ Ising and Blume-Capel models, where $s=\{1/2, 1, 3/2, 2, 5/2, 3, 7/2\}$. The mean metastable lifetime (or reversal time) is studied as a function of the applied magnetic field and for both models is found to obey the Becker-Doring theory, as was initially developed for the case of $s=1/2$ Ising ferromagnet within the classical nucleation theory. Moreover, the decay of metastable volume fraction nicely follows the Avrami's law for all values of $s$ and for both mode…
Blume-Capel model on directed and undirected Small-World Voronoi-Delaunay random lattices
利用蒙特卡罗模拟研究了具有猝灭无序的有向和无向随机晶格上自旋为1的二维Blume-Capel模型的临界性质.得到了临界温度和临界点指数。对于不规则的情况，该随机系统与规则的二维模型属于同一普适类。然而，对于有向随机晶格，对于q qc有二阶相变< qc and a first-order phase transition for q >，其中qc是临界重布线概率。计算了q < qc时的临界指数，它们与常规的二维铁磁模型不属于同一普适类。
We study the transient behavior of damage propagation in the two-dimensional spin-$1$ Blume-Capel model using Monte Carlo simulations with Metropolis dynamics. We find that, for a particular region in the second-order transition regime of the crystal field--temperature phase diagram of the model, the average Hamming distance decreases exponentially with time in the weakly damaged system. Additionally, its rate of decay appears to depend linearly on a number of Hamiltonian parameters, namely the crystal field, temperature, applied magnetic field, but also on the amount of damage. Finally, a com…
We investigate by means of Monte Carlo simulations the dynamic phase transition of the two-dimensional kinetic Blume-Capel model under a periodically oscillating magnetic field in the presence of a quenched random crystal-field coupling. We analyze the universality principles of this dynamic transition for various values of the crystal-field coupling at the originally second-order regime of the corresponding equilibrium phase diagram of the model. A detailed finite-size scaling analysis indicates that the observed nonequilibrium phase transition belongs to the universality class of the equilib…
We obtain the phase diagram for the Blume-Capel model with bimodal distribution for random crystal fields, in the space of three fields: temperature, crystal field and magnetic field. We find that three critical lines meet at a tricritical point, but only for weak disorder. As disorder strength increases there is no tricritical point in the phase diagram. We instead find a bicritical end point, where only two of the critical lines meet on a first order surface in the H=0 plane. For intermediate strengths of disorder, the phase diagram has critical end points along with the bicritical end point…
We employ numerical simulations and finite-size scaling techniques to investigate the properties of the dynamic phase transition that is encountered in the Blume-Capel model subjected to a periodically oscillating magnetic field. We mainly focus on the study of the two-dimensional system for various values of the crystal-field coupling in the second-order transition regime. Our results indicate that the present non-equilibrium phase transition belongs to the universality class of the equilibrium Ising model and allow us to construct a dynamic phase diagram, in analogy to the equilibrium case, …
We study the effect of different symmetric random field distributions: trimodal and Gaussian on the phase diagram of the infinite range Blume-Capel model. For the trimodal random field, the model has a very rich phase diagram. We find three new ordered phases, multicritical points like tricritical point (TCP), bicritical end point (BEP), critical end point (CEP) along with some multi-phase coexistence points. We also find re-entrance at low temperatures for some values of the parameters. On the other hand for the Gaussian distribution the phase diagram consists of a continuous line of transiti…
We investigate the phase diagram for the spin-$3/2$ ferromagnetic Blume-Capel model in a transverse crystal field using the standard mean-field approximation within the framework of Bogoliubov inequality for free energy. We draw a very rich phase diagram with first- and second-order transition lines; tricritical and tetracritical points; critical endpoint of order 2 and double critical endpoint. Additionally, the behaviour of magnetisation as a function of temperature over a wide range of values of both longitudinal and transverse crystal fields is also analysed. To the best of our knowledge, …
We have revisited the mean-field treatment for the Blume-Capel model under the presence of a discrete random magnetic field as introduced by Kaufman and Kanner. The magnetic field ($H$) versus temperature ($T$) phase diagrams for given values of the crystal field $D$ were recovered in accordance to Kaufman and Kanner original work. However, our main goal in the present work was to investigate the distinct structures of the crystal field versus temperature phase diagrams as the random magnetic field is varied because similar models have presented reentrant phenomenon due to randomness. Followin…
Extension of the constant exchange probability method to multi-dimensional replica exchange Monte Carlo applied to the tri-critical spin-1 Blume-Capel model
Dynamic Phase Transition in the Kinetic Spin-3/2 Blume-Capel Model: Phase Diagrams in the Temperature and Crystal-Field Interaction Plane
我们分析，在平均场的方法内，动力学自旋3/2的Blume-Capel模型的Glauber型随机动力学和随时间变化的振荡外部磁场的定态。动态相变点是通过研究动态磁化强度作为温度的函数的行为，以及计算Liapunov指数。在温度和晶场相互作用平面上构造了相图。我们发现了五种基本类型的相图的约化磁场振幅参数（h）的不同值，其中他们提出了一个无序，两个有序相和共存相区。相图还显示出0<h<1.44的动态双临界点，1.44<h 5.06的动态三临界点<5.06 and two dynamic tricritical points for h>。
We investigate the first-order transition in the spin-1 two-dimensional Blume-Capel model in square lattices by revisiting the transfer-matrix method. With large strip widths increased up to the size of 18 sites, we construct the detailed phase coexistence curve which shows excellent quantitative agreement with the recent advanced Monte Carlo results. In the deep first-order area, we observe the exponential system-size scaling of the spectral gap of the transfer matrix from which linearly increasing interfacial tension is deduced with decreasing temperature. We find that the first-order signat…
Phase transitions in a triangular Blume-Capel antiferromagnet
利用蒙特卡罗模拟研究了三角晶格上阻挫Blume-Capel（BC）反铁磁体的临界行为。对于一个减少的单离子各向异性强度$-1.47 \lesssim d < 0$，我们发现两个相变。低温相的特征是两个亚晶格上的反铁磁长程有序（LRO），第三个亚晶格保持非磁性状态。在较高的温度下，有一个临界区的Berezinskiii-Kosterlitz无（BKT）型与幂律衰减的自旋关联函数。对于$-1.5 \le d \lesssim -1.47$，从LRO到顺磁区只有一个相变，并且是一级相变。BKT相的存在下，在目前的挫折BC模型是一个新的功能，没有观察到在其非挫折的同行。的衰减指数$η$的BKT相对应的上限和较低的温度的值似乎是一致的六态时钟模型的理论预测。
