论文标题
$ ϕ^4_3 $的相转换
Phase transitions for $ϕ^4_3$
论文作者
论文摘要
我们为低温$ ϕ^4_3 $的磁性建立了一个表面顺序的大偏差估计。作为副产品，我们获得了$ ϕ^4_3 $奇异随机PDE给出的GLAUBER动力学的光谱差距的衰减。我们的主要技术贡献是$ ϕ^4_3 $的轮廓范围，它扩展了Glimm，Jaffe和Spencer（1975）的2D结果。我们调整了Bodineau，Velenik和Ioffe（2000）的论点，以使用这些轮廓界限来研究相位分离。获得轮廓边界的主要挑战是处理$ ϕ^4_3 $的紫外线差异，同时保留低温电位的结构。为此，我们基于Barashkov和Gubinelli（2019）最近开发的$ ϕ^4_3 $的紫外线稳定性方法。
We establish a surface order large deviation estimate for the magnetisation of low temperature $ϕ^4_3$. As a byproduct, we obtain a decay of spectral gap for its Glauber dynamics given by the $ϕ^4_3$ singular stochastic PDE. Our main technical contributions are contour bounds for $ϕ^4_3$, which extends 2D results by Glimm, Jaffe, and Spencer (1975). We adapt an argument by Bodineau, Velenik, and Ioffe (2000) to use these contour bounds to study phase segregation. The main challenge to obtain the contour bounds is to handle the ultraviolet divergences of $ϕ^4_3$ whilst preserving the structure of the low temperature potential. To do this, we build on the variational approach to ultraviolet stability for $ϕ^4_3$ developed recently by Barashkov and Gubinelli (2019).
