Magnetic fluctuations in the classical XY model:: The origin of an exponential tail in a complex system -: art. no. 041106
Magnetic fluctuations in the classical XY model:: The origin of an exponential tail in a complex system -: art. no. 041106
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DOI：
10.1103/physreve.63.041106
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发表时间：
2001-04-01
影响因子：
2.4
通讯作者：
Sellitto, M
中科院分区：
文献类型：
--
作者：
Bramwell, ST;Fortin, JY;Sellitto, M
研究了有限尺寸XY模型低温相磁序参量波动的概率密度函数。在二维中，这个系统在整个低温阶段都是临界的。在这种情况下，它是解析的，不依赖于尺度假设，分布是非高斯的，具有普遍形式，与系统大小和临界指数都无关。得到了分布生成函数的精确表达式，并将其与高分辨率分子动力学和蒙特卡罗模拟的数值数据进行了转换和比较。对分布的渐近线进行了计算，发现它是指数型和双指数型。计算的分布拟合到三个标准函数：从极值统计理论推广的Gumbel第一渐近线分布、广义对数正态分布和chi(2)分布。将计算扩展到一般维度，在小于4的所有维度上都存在指数尾。尽管事实上临界波动被限制在D = 2。这些结果是根据在界面生长模型和耗散系统驱动到非平衡稳态中观察到的类似行为来讨论的。
We study the probability density function for the fluctuations of the magnetic order parameter in the low-temperature phase of the XY model of finite size. In two dimensions, this system is critical over the whole of the low-temperature phase. It is shown analytically and without recourse to the scaling hypothesis that, in this case, the distribution is non-Gaussian and of universal form, independent of both system size and critical exponent eta. An exact expression for the generating function of the distribution is obtained, which is transformed and compared with numerical data from high-resolution molecular dynamics and Monte Carlo simulations. The asymptotes of the distribution are calculated and found to be of exponential and double exponential form. The calculated distribution is fitted to three standard functions: a generalization of Gumbel's first asymptote distribution from the theory of extremal statistics, a generalized log-normal distribution, and a chi (2) distribution. The calculation is extended to general dimension and an exponential tail is found in all dimensions less than 4. despite the fact that critical fluctuations are limited to D = 2. These results are discussed in the light of similar behavior observed in models of interface growth and for dissipative systems driven into a nonequilibrium steady state.