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arXiv 2012.11853cond-mat.str-el
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顺磁相海森堡磁体自旋磁化率的非解析动量依赖性及其对临界指数的影响

The non-analytic momentum dependence of spin susceptibility of Heisenberg magnets in paramagnetic phase and its effect on critical exponents

A. A. Katanin

摘要:

在任意维$2<d<4$的非线性σ模型(NLSM)中,研究了Heisenberg磁体顺磁相静态磁化率$χ(q)$的动量依赖性及其与临界行为的关系.在$1/N$展开式的一阶中,$N$是自旋分量的个数,我们发现了$χ(q)\propto[q^{2}+ξ^{-2}(1+f(qξ))]^{-1+η/2}$,其中$ξ$是关联长度,$q$是从磁波矢测量的动量,普适标度函数$f(x)$描述了与标准Landau-Ginzburg动量依赖关系的偏差。与之前在大$x$的研究一致,我们发现$f(x\gg 1)\simeq (2B_{4}/N)x^{4-d}$ ;系数$B_4$的绝对值随着$d$在$d>5/2$增加。使用NLSM,我们得到的贡献的“异常”项$ξ^{-2}f(qξ)$的临界指数$ν$,比较它的贡献的非解析依赖,起源于临界指数$η$(所获得的临界指数$ν$和$η$同意与以前的研究)。在$3\leq d<4$范围内,前者的贡献占主导地位,并在极限$d\rightarrow 4.$内完全确定了对临界指数$ν$的$1/N$修正

英文摘要:

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 $d\rightarrow 4.$

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