四维空间附近标量场的临界动力学
Critical dynamics of a scalar field near four spatial dimensions
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中文总结 AI 辅助
该研究围绕四维空间附近的标量场论，构建超对称场论表述，通过双圈展开发现传播与过阻尼极限的不动点差异，证明传播临界动力学区域对局域平衡耗散不稳定。
中文摘要 AI 辅助
非守恒序参量的临界动力学通常被认为在长程区域会出现过阻尼，即便在微观或中间尺度存在传播模式。我们研究了热平衡中标量场论的临界动力学，该理论除了包含局域摩擦和噪声外，还含有时变的二阶动能项。我们展示了如何构建超对称场论表述。利用围绕四维空间的双圈展开，我们证明传播模式和严格过阻尼极限共享相同的静态高斯不动点与Wilson-Fisher不动点，但实现了不同的动力学标度区域。过阻尼极限重现了Model A。在局域摩擦和噪声消失的曲面上，该理论支持一个相互作用的传播不动点，其动力学指数在双圈阶会受到修正。我们证明粗粒化不会在该曲面上产生局域耗散算符，因此该曲面在重整化群（RG）流下保持不变。然而，局域耗散在传播不动点处是相关的：任意小的平衡摩擦-噪声微扰都会驱动流远离传播标度。因此，传播临界动力学定义了一个自洽但需要精细调谐的区域，该区域对局域平衡耗散不稳定。
英文摘要
The critical dynamics of a non-conserved order parameter is generally expected to become overdamped at long distances, even when propagating modes occur at microscopic or intermediate scales. We investigate the critical dynamics of a scalar field theory in thermal equilibrium which, in addition to local friction and noise, also contains a time-dependent second-order kinetic term. We show how to build a supersymmetric field-theory formulation. Using a two-loop expansion about four spatial dimensions, we show that the propagating and strictly overdamped limits share the same static Gaussian and Wilson-Fisher fixed points but realize distinct dynamical scaling regimes. The overdamped limit reproduces Model A. On the surface where local friction and noise vanish, the theory instead supports an interacting propagating fixed point whose dynamic exponent receives corrections at two loops. We demonstrate that coarse-graining does not generate a local dissipative operator on this surface, which therefore remains invariant under the RG flow. Local dissipation is nevertheless relevant at the propagating fixed point: an arbitrarily small equilibrium friction-noise perturbation drives the flow away from propagating scaling. Propagating critical dynamics thus defines a consistent but fine-tuned regime that is unstable to local equilibrium dissipation.
