淬火无序系统相变的动力学研究

Real systems contain inevitably disorders, for example impurities, whose effects on phase transitions are thus of great importance. According to different strength of the interaction between spin pairs or the applied magnetic field the disorder can fall roughly into two classes: random-bond and random-field. For a three-dimensional random-bond system whose pure version undergoes a first-order phase transition, crossover effects make it hard to indentify the asymptotic critical regime controlled by the random fixed point. Moreover, there is controversy about the sign of specific heat critical exponent of the continuous phase transition induced by random bonds. While the three-dimensional random-field Ising model, as a prototypical model of site-diluted antiferromagnet in a uniform external field, has drawn a great deal of attention. However, the critical exponents of the continuous phase transition induced by random field in the different references show little agreement. On the basis of previous work from applicants this project will concentrate on three-dimensional four- and eight-state random-bond Potts model and random-bond Blume-Capel model as well as three-dimensional Gaussian random-field Ising model using finite-time scaling method in the presence of linearly varying temperature. The critical exponents so estimated independently enable us to identify asymptotic critical behavior aided by analyses on scaling laws and variations of these exponents with disorder amplitudes. Therefore, it will facilitate the understanding of the phase transition in the quenched disordered systems.

实际材料中总是含有杂质等无序，因此研究无序对相变的影响是一个重要课题。根据自旋间相互作用大小的无序或是外加磁场大小的无序可将淬火无序大致分为随机键和随机场两类。对于纯系统发生一级相变的三维随机键系统，因渡越效应的影响难以确定随机不动点控制的渐近标度区，且已有的研究工作中由随机键诱导的连续相变比热临界指数的正负存在争议。而作为均匀外场下点缺陷反铁磁体的理论模型，三维随机场Ising模型受到了广泛的关注，但不同文献所定出的随机场诱导的连续相变临界指数存在较大分歧。在申请人前期工作的基础上，本项目运用线性变温下的有限时间标度方法研究三维情况下的四态和八态随机键Potts模型、随机键Blume-Capel模型以及高斯分布随机场Ising模型，通过分析标度律以及指数随无序度的变化趋势，定出描述随机不动点的渐近临界指数，从而促进对淬火无序系统相变的理解。

本项目运用有限时间动力学方法研究了三维淬火无序系统的相变行为。对于三维q>3的随机键Potts模型而言，随着无序增加系统从一级相变经三临界点向连续相变渡越。我们导出了描述这种渡越现象的标度函数，找到了在随机诱导的连续相变区域识别渐近标度行为的一种行之有效的方法；在平均场理论框架下引入对数修正，导出了三临界点处的标度函数，并据此验证了无序系统中经典的三临界点行为；在对有效尺寸效应和代数修正分析的基础上，进一步核实了无序诱导的渐近标度区关联长度指数\nu<2/d（d是维度），这一结果反映了系统内在的渐近临界行为，而先前文献中得到的也许仅仅是有限尺寸的结果。对于三维随机场Ising模型而言，双峰分布和高斯分布的随机场情况属于同一个普适类，相应的临界指数接近实验文献的研究结果。