零温尖晶石-铁磁相变：畴壁能的标度分析
Zero-temperature spinglass-ferromagnetic transition : scaling analysis of the domain-wall energy
摘要：
对于具有平均$J_0$和单位方差的高斯随机耦合的伊辛模型，零温玻璃-铁磁转变作为控制参数$J_0$的函数可以通过定义为畴壁能量$J^R(L) \equiv E_{GS}^{(AF)}(L)-E_{GS}^{(F)}(L)$（即，在一个方向上对应于反铁磁和铁磁边界条件的基态能量之间的差）的尺寸-$J_0$依赖的重整化耦合来研究。我们研究数值模拟的临界指数，这种零温度转变内的Migdal-Kadanoff近似作为一个功能的尺寸$d=2,3,4,5,6$。然后，我们比较平均场球模型。我们的主要结论是，在低维情况下，临界刚度指数$θ^c$明显大于自旋玻璃刚度指数$θ^{SG}$，但在足够高的维度和平均场球模型中，它们是一致的。我们还讨论了重正化耦合的平均值和分布宽度的有限尺寸标度性质。
英文摘要：
For the Ising model with Gaussian random coupling of average $J_0$ and unit variance, the zero-temperature spinglass-ferromagnetic transition as a function of the control parameter $J_0$ can be studied via the size-$L$ dependent renormalized coupling defined as the domain-wall energy $J^R(L) \equiv E_{GS}^{(AF)}(L)-E_{GS}^{(F)}(L)$ (i.e. the difference between the ground state energies corresponding to AntiFerromagnetic and and Ferromagnetic boundary conditions in one direction). We study numerically the critical exponents of this zero-temperature transition within the Migdal-Kadanoff approximation as a function of the dimension $d=2,3,4,5,6$. We then compare with the mean-field spherical model. Our main conclusion is that in low dimensions, the critical stiffness exponent $θ^c$ is clearly bigger than the spin-glass stiffness exponent $θ^{SG}$, but that they turn out to coincide in high enough dimension and in the mean-field spherical model. We also discuss the finite-size scaling properties of the averaged value and of the width of the distribution of the renormalized couplings.
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