双曲晶格上不连续相变的边界场驱动控制
Boundary-field-driven control of discontinuous phase transitions on hyperbolic lattices
摘要：
研究了二维双曲格点上的多态Potts模型在各种边界效应下的动力学行为。用角转移矩阵重整化群方法计算了自由能。我们分析了收缩边界层的Potts模型在热力学极限下的相变。即使一对边界层收缩，也存在假的相变。随着收缩边界层数目的增加，它的重要性减弱，直到正确的相变（在本体内部深处）战胜错误的相变。为此目的，我们推导出一个热力学量，即所谓的体过剩自由能，它取决于收缩的边界层，并记住附加的边界效应。特别地，磁场施加在最外边界层上。在双曲晶格中，如果抑制所有的边界效应，则边界磁场不影响体相的二阶相变，而一阶（不连续的）相变对边界磁场非常敏感.与欧几里得晶格上的相变相反，双曲晶格上的不连续相变可以通过改变边界磁场来连续控制（在一定的温度共存区域内）。
英文摘要：
The multistate Potts models on two-dimensional hyperbolic lattices are studied with respect to various boundary effects. The free energy is numerically calculated by Corner Transfer Matrix Renormalization Group method. We analyze phase transitions of the Potts models in the thermodynamic limit with respect to contracted boundary layers. A false phase transition is present even if a couple of the boundary layers are contracted. Its significance weakens, as the number of the contracted boundary layers increases, until the correct phase transition (deep inside the bulk) prevails over the false one. For this purpose we derive a thermodynamic quantity, the so-called bulk excess free energy, which depends on the contracted boundary layers and memorizes additional boundary effects. In particular, the magnetic field is imposed on the outermost boundary layer. While the boundary magnetic field does not affect the second-order phase transition in the bulk if suppressing all the boundary effects on the hyperbolic lattices, the first-order (discontinuous) phase transition is significantly sensitive to the boundary magnetic field. Contrary to the phase transition on the Euclidean lattices, the discontinuous phase transition on the hyperbolic lattices can be continuously controlled (within a certain temperature coexistence region) by varying the boundary magnetic field.
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