Giuraniuc C V, Hatchett J P L, Indekeu J O, Leone M, Pérez Castillo I, Van Schaeybroeck B, Vanderzande C
Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, 3001 Leuven, Belgium.
Phys Rev Lett. 2005 Aug 26;95(9):098701. doi: 10.1103/PhysRevLett.95.098701.
Scale-free networks with topology-dependent interactions are studied. It is shown that the universality classes of critical behavior, which conventionally depend only on topology, can also be explored by tuning the interactions. A mapping, gamma'=(gamma-mu)/(1-mu), describes how a shift of the standard exponent gamma of the degree distribution P(q) can absorb the effect of degree-dependent pair interactions J(ij)proportional to(q(i)q(j))(-mu). The replica technique, cavity method, and Monte Carlo simulation support the physical picture suggested by Landau theory for the critical exponents and by the Bethe-Peierls approximation for the critical temperature. The equivalence of topology and interaction holds for equilibrium and nonequilibrium systems, and is illustrated with interdisciplinary applications.
研究了具有拓扑依赖相互作用的无标度网络。结果表明，传统上仅依赖于拓扑结构的临界行为普适类，也可以通过调整相互作用来探索。一个映射关系γ′ = (γ - μ)/(1 - μ)，描述了度分布P(q)的标准指数γ的偏移如何能够吸收与(q(i)q(j))^(-μ)成正比的度依赖对相互作用J(ij)的影响。副本技术、腔方法和蒙特卡罗模拟支持了朗道理论对临界指数以及贝特 - 皮尔斯近似对临界温度所提出的物理图像。拓扑和相互作用的等价性在平衡和非平衡系统中均成立，并通过跨学科应用进行了说明。
