Ising's Roots and the Transfer-Matrix Eigenvalues.

Today, the Ising model is an archetype describing collective ordering processes. As such, it is widely known in physics and far beyond. Less known is the fact that the thesis defended by Ernst Ising 100 years ago (in 1924) contained not only the solution of what we call now the 'classical 1D Ising model' but also other problems.

The diaspora model for human migration.

Migration's impact spans various social dimensions, including demography, sustainability, politics, economy, and gender disparities. Yet, the decision-making process behind migrants choosing their destination remains elusive. Existing models primarily rely on population size and travel distance to explain the spatial patterns of migration flows, overlooking significant population heterogeneities.

Individual bias and fluctuations in collective decision making: from algorithms to Hamiltonians.

In this paper, we reconsider the spin model suggested recently to understand some features of collective decision making among higher organisms (Hartnett2016038701). Within the model, the state of an agentis described by the pair of variables corresponding to its opinionSi=±1and a biastoward any of the opposing values of. Collective decision making is interpreted as an approach to the equilibrium state within the nonlinear voter model subject to a social pressure and a probabilistic algorithm.

Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws.

We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e.

Self-averaging in the random two-dimensional Ising ferromagnet.

We study sample-to-sample fluctuations in a critical two-dimensional Ising model with quenched random ferromagnetic couplings. Using replica calculations in the renormalization group framework we derive explicit expressions for the probability distribution function of the critical internal energy and for the specific heat fluctuations. It is shown that the disorder distribution of internal energies is Gaussian, and the typical sample-to-sample fluctuations as well as the average value scale with the system size L like ∼Llnln(L).

Universal free-energy distribution in the critical point of a random Ising ferromagnet.

We discuss the non-self-averaging phenomena in the critical point of weakly disordered Ising ferromagnet. In terms of the renormalized replica Ginzburg-Landau Hamiltonian in dimensions D<4, we derive an explicit expression for the probability distribution function (PDF) of the critical free-energy fluctuations. In particular, using known fixed-point values for the renormalized coupling parameters, we obtain the universal curve for such PDF in the dimension D=3.