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首页> 外文期刊>Physical review >One-loop functional renormalization group study for the dimensional reduction and its breakdown in the long-range random field O(N) spin model near lower critical dimension
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One-loop functional renormalization group study for the dimensional reduction and its breakdown in the long-range random field O(N) spin model near lower critical dimension

机译：一环功能重整化组研究在下临界尺寸附近的远程随机场O（N）自旋模型中的尺寸缩减及其分解

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We consider the random-field O(N) spin model with long-range exchange interactions which decay with distance r between spins as r(-d-sigma) and/or random fields which correlate with distance r as r(-d+rho), and reexamine the critical phenomena near the lower critical dimension by use of the perturbative functional renormalization group. We compute the analytic fixed points in the one-loop beta functions, and study their stability. We also calculate the critical exponents at the analytical fixed points. We show that the analytic fixed point which governs the phase transition in the system with the long-range correlations of random fields can be destabilized by the nonanalytic perturbation in both cases where the exchange interactions between spins are short ranged and long ranged. For the system with the long-range exchange interactions and uncorrelated random fields, we show that the d - d - sigma dimensional reduction at the leading order of the d - 2 sigma expansion holds only for N 2(4 + 3 root 3) similar or equal to 18.3923.... Our investigation into the system with the long-range exchange interactions and uncorrelated random fields also gives the value of the boundary between critical behaviors in systems with long-range and short-range exchange interactions, which is identical to that predicted by Sak [Phys. Rev. B 8, 281 (1973)]. For the system with the long-range exchange interactions and the long-range correlated random fields, we show that the d - d - sigma - rho dimensional reduction does not hold within the present framework, as far as N is finite.
机译：我们考虑具有远距离交换相互作用的随机场O（N）自旋模型，该模型随着自旋之间的距离r衰减为r（-d-sigma）和/或与距离r相关的随机场为r（-d + rho ），并使用微扰功能重整化组重新检查下临界尺寸附近的临界现象。我们计算一环beta函数中的解析不动点，并研究其稳定性。我们还计算了分析固定点处的临界指数。我们表明，在自旋之间的交换相互作用是短距离的和长距离的两种情况下，通过非解析扰动可以使控制系统中相变的解析不动点不稳定，该非固定扰动使系统具有固定的相变。对于具有长距离交换相互作用和不相关随机场的系统，我们表明d-> d-sigma降维在d-2 sigma扩展的前导顺序中仅对N> 2（4 + 3根3）有效）等于或等于18.3923 ....我们对具有长距离交换相互作用和不相关随机场的系统的研究也给出了具有长距离和短距离交换相互作用的系统中关键行为之间的边界值。与Sak [Phys。 Rev. B 8，281（1973）]。对于具有远距离交换相互作用和远距离相关随机场的系统，我们证明只要N是有限的，d-> d-sigma-rho降维在当前框架内不成立。

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    《Physical review》 |2019年第2期|024412.1-024412.14|共14页
  • 作者

    Sakamoto Yoshinori;

  • 作者单位

    Nihon Univ, Coll Sci & Technol, Lab Phys, 7-24-1 Narashino Dai, Funabashi, Chiba 2748501, Japan;

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