标题： O(4)标量模型中的自发对称性破缺 显示英文标题

标题： Spontaneous symmetry breaking in the O(4) scalar model on a lattice

摘要： 在零温度下，四组分四维标量$\lambda \phi^4_4$模型（O(4)模型）的自发对称性破缺在不同耦合常数$\lambda$下被研究。开发了一种处理此类依赖性的通用方法。通过鞍点法，在标量场的内部空间中使用球坐标积分出戈德斯通模，从而将该模型的初始泛函积分简化为便于晶格研究的有效单组分理论。该理论的配分函数在静态极限下被解析计算，并表现出$\lambda$依赖性，这有助于区分对称性破缺。使用 QCDGPU 软件包在 HGPU 集群上进行了蒙特卡洛模拟。结果表明，对于$\lambda>\lambda_0 \simeq 10^{-5}$，对称性被自发破缺。对于较小的耦合值，标量场在晶格上消失，这可以解释为均匀凝聚体的不稳定性，甚至是模型本身的不稳定性。临界值$\lambda_0$独立于所研究的晶格尺寸$16^4$和$32^4$。 显示英文摘要

摘要： The spontaneous symmetry breaking at zero temperature in the four-component four-dimensional scalar $\lambda \phi^4_4$ model (the O(4) model) is investigated on a lattice for different values of the coupling constant $\lambda$. A general method for dealing with such type dependence is developed. The Goldstone modes are integrated out in the spherical coordinates in the internal space of the scalar field by the saddle point method, and the initial functional integral of the model is reduced to an effective one-component theory convenient for lattice investigations. The partition function of this theory is calculated analytically in the static limit and demonstrates the $\lambda$-dependence which is characteristic for distinguishing symmetry breaking. Monte Carlo simulations are performed with the QCDGPU software package on a HGPU cluster. It is shown that the symmetry is spontaneously broken for $\lambda>\lambda_0 \simeq 10^{-5}$. For smaller coupling values, the scalar field vanishes on a lattice, which can be interpreted as instability of the homogeneous condensate or even instability of the model itself. The critical value $\lambda_0$ is independent of the lattice sizes $16^4$ and $32^4$ investigated.