随机介质中界面生长可解模型中脱钉时的形态转变
Morphology transition at depinning in a solvable model of interface growth in a random medium
摘要：
我们提出了一个简单的，精确可解的，在一个随机介质中，是一个变种的零温度随机场伊辛模型的凯莱树界面生长模型。该模型被证明有一个相图（临界脱钉场与无序强度）定性类似的数值上得到的立方晶格。然后，我们引入一个专门定制的随机图，允许一个精确的渐近分析的高度和宽度的接口。我们表征的界面的形态的变化作为一个功能的无序强度，发现发生在一个多临界点沿脱钉过渡线的变化。
英文摘要：
We propose a simple, exactly solvable, model of interface growth in a random medium that is a variant of the zero-temperature random-field Ising model on the Cayley tree. This model is shown to have a phase diagram (critical depinning field versus disorder strength) qualitatively similar to that obtained numerically on the cubic lattice. We then introduce a specifically tailored random graph that allows an exact asymptotic analysis of the height and width of the interface. We characterize the change of morphology of the interface as a function of the disorder strength, a change that is found to take place at a multicritical point along the depinning-transition line.
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