论文标题
在欧几里得量子$λφ^{4} _ {d+1} $模型中恢复自发折断的对称性
Restoration of a Spontaneously Broken Symmetry in an Euclidean Quantum $λφ^{4}_{d+1}$ model with Quenched Disorder
论文作者
论文摘要
我们研究了由欧几里得量子$λφ^{4} _ {d+1} $具有淬火障碍的模型描述的自发损坏的对称阶段的低温行为。使用串联表示，根据分区函数的力矩，平均相关功能的平均产生功能，我们研究了与标量场线性耦合的疾病的效果。为了处理虚假时间的密切相关性疾病，我们在$ d $维空间中定义的模型与假想时间与统计场理论模型在空间$ {\ mathbb r}^{d}^{d} {d} \ times s^{1} $ a anisotropic quenched quenched recnenched疾病上定义。接下来，使用分数衍生物和随机微分方程，我们在树级别获得了无序系统相关函数的傅立叶变换。在一环的近似中，我们证明分区函数的矩矩可以构成关键行为。在纯系统的临界温度以下，在有序阶段的大部分，有大量的临界温度将这些矩从秩序中的每一个中的每一个中的每一个都带到一个阶段。我们显示了系统中通用量表不变性的出现。
We investigate the low temperature behavior of a system in a spontaneously broken symmetry phase described by an Euclidean quantum $λφ^{4}_{d+1}$ model with quenched disorder. Using a series representation for the averaged generating functional of connected correlation functions in terms of the moments of the partition function, we study the effects of the disorder linearly coupled to the scalar field. To deal with the strongly correlated disorder in imaginary time, we employthe equivalence between the model defined in a $d$-dimensional space with imaginary time with the statistical field theory model defined on a space ${\mathbb R}^{d}\times S^{1}$ with anisotropic quenched disorder. Next, using fractional derivatives and stochastic differential equations we obtain at tree-level the Fourier transform of the correlation functions of the disordered system. In one-loop approximation, we prove that there is a denumerable collection of moments of the partition function that can develop critical behavior. Below the critical temperature of the pure system, with the bulk in the ordered phase, there are a large number of critical temperatures that take each of these moments from an ordered to a disordered phase. We show the emergence of generic scale invariance in the system.
