标题： 稀薄图上的自旋玻璃 显示英文标题

标题： Spin Glasses on Thin Graphs

摘要： 在最近的一篇论文中，我们通过模拟发现强有力的证据表明，伊辛反铁磁体在“稀薄”随机图（费曼图）上表现出平均场自旋玻璃相变。 考虑这类随机图的固有兴趣在于它们能够提供平均场结果，而无需长程相互作用，也不存在源自Bethe格子边界问题的缺点。 在这篇文章中，我们将重新审视费曼图上伊辛模型和Potts模型的铁磁性、反铁磁性和自旋玻璃的鞍点计算。 我们使用分歧理论的标准结果，这使我们能够处理任意数量的副本以及任意的淬火键分布。 我们注意到由此计算出的铁磁性和自旋玻璃相变温度与Bethe格子类比或先前复制计算得出的结果是一致的。 然后，我们数值研究了具有正负J键分布的伊辛模型和Q=3,4,10,50状态Potts模型的自旋玻璃，特别关注伊辛情况下单个键的正负分数对自旋玻璃相变的影响，以及所有模型中重叠分布的定性形式。 文章还指出，无论是解析计算还是模拟，都与无限范围自旋玻璃模型存在相似之处。 显示英文摘要

摘要： In a recent paper we found strong evidence from simulations that the Isingantiferromagnet on ``thin'' random graphs - Feynman diagrams - displayed amean-field spin glass transition. The intrinsic interest of considering such random graphs is that they give mean field results without long range interactions or the drawbacks, arising from boundary problems, of the Bethe lattice. In this paper we reprise the saddle point calculations for the Ising and Potts ferromagnet, antiferromagnet and spin glass on Feynman diagrams. We use standard results from bifurcation theory that enable us to treat an arbitrary number of replicas and any quenched bond distribution. We note the agreement between the ferromagnetic and spin glass transition temperatures thus calculated and those derived by analogy with the Bethe lattice, or in previous replica calculations. We then investigate numerically spin glasses with a plus or minus J bond distribution for the Ising and Q=3,4,10,50 state Potts models, paying particular attention to the independence of the spin glass transition from the fraction of positive and negative bonds in the Ising case and the qualitative form of the overlap distribution in all the models. The parallels with infinite range spin glass models in both the analytical calculations and simulations are pointed out.