Nienhuis Bernard, Guo Wenan, Blöte Henk W J
Instituut voor Theoretische Fysica, Universiteit van Amsterdam, Valckenierstraat 65, The Netherlands.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Dec;78(6 Pt 1):061104. doi: 10.1103/PhysRevE.78.061104. Epub 2008 Dec 5.
We show that the exactly solved low-temperature branch of the two-dimensional O(n) model is equivalent to an O(n) model with vacancies and a different value of n . We present analytic results for several universal parameters of the latter model, which is identified as a tricritical point. These results apply to the range n</=32 and include the exact tricritical point, the conformal anomaly, and a number of scaling dimensions, among which are the thermal and magnetic exponents, and the exponent associated with the crossover to ordinary critical behavior and to tricritical behavior with cubic symmetry. We describe the translation of the tricritical model in a Coulomb gas. The results are verified numerically by means of transfer-matrix calculations. We use a generalized ADE model as an intermediary and present the expression of the one-point distribution function in that language. The analytic calculations are done both for the square and the honeycomb lattice.
我们表明，二维O(n)模型的精确求解低温分支等同于具有空位且n值不同的O(n)模型。我们给出了后一种模型几个通用参数的解析结果，该模型被确定为一个三临界点。这些结果适用于n≤32的范围，包括精确的三临界点、共形反常以及一些标度维数，其中有热指数和磁指数，以及与向普通临界行为和具有立方对称性的三临界行为转变相关的指数。我们描述了三临界模型在库仑气体中的变换。通过转移矩阵计算对结果进行了数值验证。我们使用广义ADE模型作为中介，并以该语言给出单点分布函数的表达式。对正方形晶格和蜂窝晶格都进行了解析计算。
