STATIC AND DYNAMIC CRITICAL PHENOMENA OF THE TWO-DIMENSIONAL Q-STATE POTTS-MODEL
STATIC AND DYNAMIC CRITICAL PHENOMENA OF THE TWO-DIMENSIONAL Q-STATE POTTS-MODEL
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DOI：
10.1007/bf01007636
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发表时间：
1981-01-01
影响因子：
1.6
通讯作者：
BINDER, K
中科院分区：
文献类型：
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作者：
BINDER, K
通过蒙特卡罗模拟研究了q= 3,4,5,6的方形晶格上的q态Potts模型。在临界点处的能量和自由能与Kiharaet和Baxter的精确结果非常吻合。q=3的临界指数估计为α≈0.4,β≈0.1,γ≈1.45，与高温序列外推法和实空间重整化群方法基本一致。发现forq= 5,6的转变是一个非常弱的一阶转变，即出现明显的“伪临界”现象，比热、磁化率等在一阶转变温度下（几乎）发散。与动力学Ising模型一样，将动力学与模型联系起来，并研究了阶参量和能量的非线性慢化。动态指数估计为Δ (=zv)≈1.9。在我们的精度范围内，没有检测到任何依赖性。发现弛豫与动态尺度预测一致，并估计了与非线性弛豫相关的动态尺度函数。
Theq-state Potts model on the square lattice is studied by Monte Carlo simulation forq=3, 4, 5, 6. Very good agreement is obtained with exact results of Kiharaet al.and Baxter for energy and free energy at the critical point. Critical exponent estimates forq=3 areα≈0.4,β≈0.1,γ≈1.45, in rough agreement with high-temperature series extrapolation and real space renormalization-group methods. The transition forq=5, 6 is found to be a very weakly first-order transition, i.e., pronounced “pseudocritical” phenomena occur, specific heat, susceptibility, etc. (nearly) diverge at the first-order transition temperature. Dynamics is associated to the model in the same way as for the kinetic Ising model, and the nonlinear slowing down of the order parameter and of the energy is studied. The dynamic exponent is estimated to be Δ (=zv)≈1.9. Within our accuracy noqdependence is detected. The relaxation is found to be consistent with dynamic scaling predictions, and dynamic scaling functions associated with the nonlinear relaxation are estimated.