论文标题
零温度软的非谐波自旋眼镜的现场理论
Field theory for zero temperature soft anharmonic spin glasses in a field
论文作者
论文摘要
我们在一个场中引入了有限的尺寸Anharmonic软旋转玻璃，并展示了它如何在零温度和相应的环路扩展下构建场理论。该模型的平均场水平与最近引入的完全连接的模型KHGPS模型一致，并且它在零温度下的磁场中具有自旋玻璃转变，这是由于伪造的非线性激发的出现而驱动的。我们分析了该理论的零温度极限以及裸体质量和耦合在接近平均场零温度临界点方面的行为。着眼于场理论的所谓复制子部门，我们表明，与该部门波动相对应的裸质量在某个控制参数空间的某个区域的过渡时严格为正。同时，两个相关的立方耦合常数$ g_1 $和$ g_2 $在其光秃秃的价值中显示出非分析行为：在零温度下接近临界点，$ g_1 \ to \ infty $，而$ g_2 \ propto propto t $在过渡时以预先攻击的差异。沿着相同的线路，我们还开发了田间理论，以研究有限维度的模型状态的密度。我们表明，在平均场中，状态的密度会收敛到KHGPS模型之一。但是，该构建允许在扰动理论中处理有限维效应。
We introduce a finite dimensional anharmonic soft spin glass in a field and show how it allows the construction a field theory at zero temperature and the corresponding loop expansion. The mean field level of the model coincides with a recently introduced fully connected model, the KHGPS model, and it has a spin glass transition in a field at zero temperature driven by the appearance of pseudogapped non-linear excitations. We analyze the zero temperature limit of the theory and the behavior of the bare masses and couplings on approaching the mean field zero temperature critical point. Focusing on the so called replicon sector of the field theory, we show that the bare mass corresponding to fluctuations in this sector is strictly positive at the transition in a certain region of control parameter space. At the same time the two relevant cubic coupling constants $g_1$ and $g_2$ show a non-analytic behavior in their bare values: approaching the critical point at zero temperature, $g_1\to \infty$ while $g_2\propto T$ with a prefactor diverging at the transition. Along the same lines we also develop the field theory to study the density of states of the model in finite dimension. We show that in the mean field limit the density of states converges to the one of the KHGPS model. However the construction allows a treatment of finite dimensional effects in perturbation theory.
