广义多组分Widom-Rowlinson模型中的重入无序-无序转变
Reentrant disorder-disorder transitions in generalized multicomponent Widom-Rowlinson models
摘要：
在多组分Widom-Rowlinson（WR）模型的晶格版本中，每个位置可以是空的，也可以被$M$不同粒子中的一个单独占据，所有粒子都具有相同的逸度$z$。唯一非零的相互作用势是不同粒子之间的最近邻硬核排斥。对于$M<M_0$，其最小$M_0$取决于晶格结构，当$z$从0增加到$\infty$时，存在从无序（气相）相到分层（液相）相的直接转变，其中在$z>z_d(M)$处具有一个主要组分。如果是$M\ge M_0$，则在$z_c(M)$和$z_d(M)$之间存在由熵驱动的$z$的中间有序“晶相”（由两个不等价的偶数和奇数亚晶格组成）。我们推广的多组分WR模型取代硬核排斥不同粒子之间的更现实的大（但有限）排斥。该模型在任意配位数的Bethe格上精确求解。基于角转移矩阵重整化群，对二维正方晶格进行了数值计算。对$M=4$的计算结果表明，对于任意大的有限斥力，从无序气体到分层相的二级相变变为一级相变。$M\ge M_0$的结果表明，随着排斥力的减弱，晶相区本身也在缩小。对于足够弱的排斥，晶体相和分层相之间的直接跃迁变成了一对独立的晶体-气体和气体-分层跃迁;这是通过有序晶体相的无序-无序重入跃迁的一个例子。如果不同物种之间的排斥力太弱，则晶相从相图中消失。证明了广义WR模型属于Ising普适类。
英文摘要：
In the lattice version of the multicomponent Widom-Rowlinson (WR) model, each site can be either empty or singly occupied by one of $M$ different particles, all species having the same fugacity $z$. The only nonzero interaction potential is a nearest-neighbor hard-core exclusion between unlike particles. For $M<M_0$ with some minimum $M_0$ dependent on the lattice structure, as $z$ increases from 0 to $\infty$ there is a direct transition from the disordered (gas) phase to a demixed (liquid) phase with one majority component at $z>z_d(M)$. If $M\ge M_0$, there is an intermediate ordered "crystal phase" (composed of two nonequivalent even and odd sublattices) for $z$ lying between $z_c(M)$ and $z_d(M)$ which is driven by entropy. We generalize the multicomponent WR model by replacing the hard-core exclusion between unlike particles by more realistic large (but finite) repulsion. The model is solved exactly on the Bethe lattice with an arbitrary coordination number. The numerical calculations, based on the corner transfer matrix renormalization group, are performed for the two-dimensional square lattice. The results for $M=4$ indicate that the second-order phase transitions from the disordered gas to the demixed phase become of first order, for an arbitrarily large finite repulsion. The results for $M\ge M_0$ show that, as the repulsion weakens, the region of crystal phase diminishes itself. For weak enough repulsions, the direct transition between the crystal and demixed phases changes into a separate pair of crystal-gas and gas-demixed transitions; this is an example of a disorder-disorder reentrant transition via an ordered crystal phase. If the repulsion between unlike species is too weak, the crystal phase disappears from the phase diagram. It is shown that the generalized WR model belongs to the Ising universality class.
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