论文标题
海森堡磁体在顺磁性相及其对关键指数的影响的自旋敏感性的非分析动量依赖性
The non-analytic momentum dependence of spin susceptibility of Heisenberg magnets in paramagnetic phase and its effect on critical exponents
论文作者
论文摘要
我们研究了海森堡磁体的顺磁相的静态磁化易感性$χ（Q）$的动量依赖性及其在任意维度$ 2 <d <4 $的非线性Sigma模型（NLSM）中与关键行为的关系。在$ 1/n $扩展的第一阶，其中$ n $是旋转组件的数量，我们发现$χ（q）\ propto [q^{2}+ξ^{ - 2} { - 2}（1+f（q q配（q配e（q配q） $ f（x）$描述了与标准Landau-Ginzburg动量依赖的偏差。与以前的大型$ x $的研究一致，我们发现$ f（x \ gg 1）\ simeq（2b_ {4}/n）x^{4-d} $;系数$ b_4 $的绝对值增加，$ d $在$ d> 5/2 $中增加。 Using NLSM, we obtain the contribution of the"anomalous" term $ξ^{-2}f(qξ)$ to the critical exponent $ν$, comparing it to the contribution of the non-analytical dependence, originating from the critical exponent $η$ (the obtained critical exponents $ν$ and $η$ agree with previous studies).在$ 3 \ 3 \ leq d <4 $的范围内，我们发现以前的贡献占主导地位，并完全确定$ 1/n $校正对关键指数$ν$的限制$ d \ rightarrow 4. $
We study momentum dependence of static magnetic susceptibility $χ(q)$ in paramagnetic phase of Heisenberg magnets and its relation to critical behavior within nonlinear sigma model (NLSM) at arbitrary dimension $2<d<4$. In the first order of $1/N$ expansion, where $N$ is the number of spin components, we find $χ(q)\propto[q^{2}+ξ^{-2}(1+f(qξ))]^{-1+η/2}$, where $ξ$ is the correlation length, $q$ is the momentum, measured from magnetic wave vector, the universal scaling function $f(x)$ describes deviation from the standard Landau-Ginzburg momentum dependence. In agreement with previous studies at large $x$ we find $f(x\gg 1)\simeq (2B_{4}/N)x^{4-d}$; the absolute value of the coefficient $B_4$ increases with $d$ at $d>5/2$. Using NLSM, we obtain the contribution of the"anomalous" term $ξ^{-2}f(qξ)$ to the critical exponent $ν$, comparing it to the contribution of the non-analytical dependence, originating from the critical exponent $η$ (the obtained critical exponents $ν$ and $η$ agree with previous studies). In the range $3\leq d<4$ we find that the former contribution dominates, and fully determines $1/N$ correction to the critical exponent $ν$ in the limit $d\rightarrow 4.$
