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Ising model
About: Ising model is a research topic. Over the lifetime, 25508 publications have been published within this topic receiving 555000 citations.
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TL;DR: An anomalous behavior of the magnetization, magnetic susceptibility and specific heat, when P(k) is fat tailed, or, loosely speaking, when the fourth moment of the distribution diverges in infinite networks is observed.
Abstract: We find the exact critical temperature T(c) of the nearest-neighbor ferromagnetic Ising model on an "equilibrium" random graph with an arbitrary degree distribution P(k). We observe an anomalous behavior of the magnetization, magnetic susceptibility and specific heat, when P(k) is fat tailed, or, loosely speaking, when the fourth moment of the distribution diverges in infinite networks. When the second moment becomes divergent, T(c) approaches infinity, the phase transition is of infinite order, and size effect is anomalously strong.
276 citations
TL;DR: In this paper, the authors studied the critical two-dimensional Ising model with a defect line (altered bond strength along a line) in the continuum limit, and they found the complete spectrum of boundary operators, exact two-point correlation functions and the universal term in the free energy of the defect line for arbitrary strength.
276 citations
TL;DR: In this paper, a numerical method was developed to study the scaling of distribution of couplings of highly random antiferromagnetic Ising and quantum Heisenberg spin-\textonehalf{} systems.
Abstract: A numerical method is developed to study the scaling of distribution of couplings of highly random antiferromagnetic Ising and quantum Heisenberg spin-\textonehalf{} systems. The method shows how freezing into inert local singlets prevents ordering down to temperatures well below the median nearest-neighbor coupling or bare exchange percolation threshold in positionally disordered systems with Heisenberg exchange varying exponentially with distance (e.g., doped semiconductors, quasi one-dimensional salts). This is contrasted with the Ising system.
275 citations
TL;DR: In this article, an exact solvable modification of the planar Ising ferromagnet is proposed which has a roughening transition below the Curie temperature, which confirms the de Gennes-Fisher scaling theory of correlations with homogeneous surface fields.
Abstract: An exactly solvable modification of the planar Ising ferromagnet is proposed which has a roughening transition below the Curie temperature. The computation confirms the de Gennes-Fisher scaling theory of correlations with homogeneous surface fields, giving an exponent value ${\ensuremath{\Delta}}_{1}=\frac{1}{2}$.
275 citations
274 citations