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The mixed spin-1/2 and spin-3/2 Ising model on the extended Kagom\'e lattice is solved by establishing a mapping correspondence with the eight-vertex model. Letting the parameter of uniaxial single-ion anisotropy tend to infinity, the model…
We consider the planar Ising model in a finite square box and we replace the temperature parameter with a function depending on the magnetization. This creates a feedback from the spin configuration onto the parameter, which drives the…
A new method for locating analytically critical temperatures is discussed. It is exact for selfdual systems. When applied the two coupled layers of Ising spins it deviates from our preliminary Monte Carlo estimates by 1.5 standard…
We derive exact critical-temperature bounds for the classical ferromagnetic Ising model on two-dimensional periodic tessellations of the plane. For any such tessellation or lattice, the critical temperature is bounded from above by a…
Based on a high temperature expansion, we compute the two-point correlation function and the critical line of an Ising lattice gas driven into a non-equilibrium steady state by a uniform bias E. The lowest nontrivial order already…
We prove a long-standing conjecture on random-cluster models, namely that the critical point for such models with parameter $q\geq1$ on the square lattice is equal to the self-dual point $p_{sd}(q) = \sqrt q /(1+\sqrt q)$. This gives a…
We construct a model of short-range interacting Ising spins on a translationally invariant two-dimensional lattice that mimics a reversible circuit that multiplies or factorizes integers, depending on the choice of boundary conditions. We…
For a large class of repulsive interaction models, the Mayer cluster integrals can be transformed into a tridiagonal real symmetric matrix $R_{mn}$, whose elements converge to two constants. This allows for an effective extrapolation of the…
The critical behavior of a hybrid spin-electron model with localized Ising spins placed on nodal sites and mobile electrons delocalized over bonds between two nodal lattice sites is analyzed by the use of a generalized decoration-iteration…
Transfer-matrix methods, with the help of finite-size scaling and conformal invariance concepts, are used to investigate the critical behavior of two-dimensional square-lattice Ising spin-1/2 systems with first- and second-neighbor…
Based on the foundations of thermodynamics and the equilibrium conditions for the coexistence of two phases in a magnetic Ising-like system, we show, first, that there is a critical point where the isothermal susceptibility diverges and the…
We employ the microcanonical inflection-point analysis method, developed for the systematic identification and classification of phase transitions in systems of any size, to study the two-dimensional Ising model at various lattice sizes and…
We calculate high-temperature graph expansions for the Ising spin glass model with 4 symmetric random distribution functions for its nearest neighbor interaction constants J_{ij}. Series for the Edwards-Anderson susceptibility \chi_EA are…
We study a one-dimensional spin-$1/2$ model with three-spin interactions and a transverse magnetic field $h$. The model has a $Z_2 \times Z_2$ symmetry, and a duality between $h$ and $1/h$. The self-dual point at $h=1$ is a quantum critical…
We employ the numerical linked-cluster expansion to study finite-temperature properties of the uniform cubic lattice Hubbard model in the thermodynamic limit for a wide range of interaction strengths and densities. We carry out the…
A star-triangle mapping transformation is used to establish an exact correspondence between the spin-1/2 Ising model on the Shastry-Sutherland (orthogonal-dimer) lattice and respectively, the spin-1/2 Ising model on a bathroom tile (4-8)…
We apply a new updating algorithm scheme to investigate the critical behavior of the two-dimensional ferromagnetic Ising model on a triangular lattice with nearest neighbour interactions. The transition is examined by generating accurate…
We show that atoms in tilted optical superlattices provide a platform for exploring coupled spin chains of forms that are not present in other systems. In particular, using a period-2 superlattice in 1D, we show that coupled Ising spin…
We study the mutual information between two lattice-blocks in terms of von Neumann entropies for one-dimensional infinite lattice systems. Quantum $q$-state Potts model and transverse field spin-$1/2$ XY model are considered numerically by…
The critical behavior of the Ising model on a fractal lattice, which has the Hausdorff dimension $\log_{4} 12 \approx 1.792$, is investigated using a modified higher-order tensor renormalization group algorithm supplemented with automatic…