We consider the symmetric two-state 16-vertex model on the square lattice whose vertex weights are invariant under any permutation of adjacent edge states. The vertex-weight parameters are restricted to a critical manifold which is self-dual under the gauge transformation. The critical properties of the model are studied numerically by using the Corner Transfer Matrix Renormalization Group method. Accuracy of the method is tested on two exactly solvable cases: the Ising model and a specific version of the Baxter 8-vertex model in a zero field that belong to different universality classes. Numerical results show that the two exactly solvable cases are connected by a line of critical points with the polarization as the order parameter. There are numerical indications that critical exponents vary continuously along this line in such a way that the weak universality hypothesis is violated.
We prove the validity of multiparameter universality for the exact critical bulk correlation functions of the anisotropic square-lattice and triangular-lattice Ising models on the basis of the exact scaling structure of the correlation function of the two-dimensional anisotropic scalar $φ^4$ model with four nonuniversal parameters. The correlation functions exhibit a directional nonuniversality due to principal axes whose orientation depends on microscopic details. In particular we determine the exact anisotropy matrices governing the bulk and finite-size critical behavior of the $φ^4$ and Isi…
We implement parallel versions of the GARM and Wang-Landau algorithms for stars and for acyclic uniform branched networks in the square lattice. These are models of monodispersed branched polymers, and we estimate the star vertex exponents $σ_f$ for $f$-stars, and the entropic exponent $γ_\mathcal{G}$ for networks with comb and brush connectivity in two dimensions. Our results verify the predicted (but not rigorously proven) exact values of the vertex exponents and we test the scaling relation [5] $$ γ_{\mathcal{G}}-1 = \sum_{f\geq 1} m_f \, σ_f $$ for the branched networks in two dimensions.
Weak universality, bicritical points and reentrant transitions in the critical behaviour of a mixed spin-1/2 and spin-3/2 Ising model on the union jack (centered square) lattice
In the present Letter we discuss the origin of the vertex population inversion observed experimentally in the mediated Artificial Square Ice. An interaction modifier is a disc-shaped magnetic nanoisland (a dot) which is placed at the center of a vertex to mediate the interaction between the nearby islands. We show that the inversion is of entropic origin, and can be explained via the renormalization of the vertex configuration energies due to local interaction between the nanoislands and the dot. We show it in a model with mixed Heisenberg and Ising spins (a spin-dot interaction) that as a fun…
Folding transitions of the square--diagonal two--dimensional lattice
用集团变分法研究了P. Di Francesco（Nucl.Phys.B525，5071998）提出的一个顶点模型的相图，该模型描述了一个正方形晶格的构型，该晶格可以沿主轴和对角线以不同的弯曲能折叠.发现了一个非常丰富的结构，包括部分折叠相和完全折叠相，不同的无序相和一个平坦相，无序相和平坦相之间的褶皱转变是一级的。通过对基态的分析和对模型简化为伊辛模型的两个极限的分析，证实了CVM的结果。
Transfer matrices and partition-function zeros for antiferromagnetic Potts models. VI. Square lattice with special boundary conditions
使用转移矩阵方法，研究了零温度下正方形晶格q态Potts反铁磁物质（=正方形晶格色多项式）的配分函数零点，这些配分函数零点是从具有自由边界条件的m x n网格中通过邻接最左列中所有位点的一个新顶点和邻接最右列中所有位点的第二个新顶点获得的。我们提供的数值证据表明，配分函数的零变得密集的限制曲线B_ \infty（sq）外的复q平面上的普通（如自由或圆柱）边界条件的模型。尽管如此，无限体积自由能在这个区域是完全解析的。
The transfer matrix of the square-lattice eight-vertex model on a strip with $L\geqslant 1$ vertical lines and open boundary conditions is investigated. It is shown that for vertex weights $a,b,c,d$ that obey the relation $(a^2+ab)(b^2+ab)=(c^2+ab)(d^2+ab)$ and appropriately chosen $K$-matrices $K^\pm$ this transfer matrix possesses the remarkably simple, non-degenerate eigenvalue $Λ_L = (a+b)^{2L}\,\text{tr}(K^+K^-)$. For positive vertex weights, $Λ_L$ is shown to be the largest transfer-matrix eigenvalue. The corresponding eigenspace is equal to the space of the ground states of the Hamilton…
