Spontaneous magnetization of Kagome lattice in Ising model

The spontaneous magnetization of the Kagome lattice in the Ising model is investigated. The proof of the fallacy of spontaneous magnetization obtained earlier and repeatedly migrating from publication to publication is given. An exact expression is presented in the standard Onsager form for spontaneous magnetization in the anisotropic case (depending on arbitrary values and signs of exchange interactions in all three directions in the Kagome lattice)

Frustrations on decorated triangular lattice in Ising model

We study the frustration properties of the Ising model on a decorated triangular lattice with an arbitrary number of decorating spins on all lattice bonds in the framework of an exact analytical approach based on the Kramers--Wannier transfer matrix method. Expressions for the entropy, heat capacity, and spontaneous magnetization of the lattice are obtained, including the residual (zero-temperature) entropy and residual (zero-temperature) spontaneous magnetization of the system. The existence of magnetic frustrations in such a model and their influence on the behavior of the thermodynamic functions of the system are shown. The new and most important result of our study is related to the description of the possible coexistence of frustrations and long-range magnetic order in partially ordered spin systems

Critical phenomena in 1D Ising model with arbitrary spin

The aim of this work was to study critical phenomena taking place in 1D Ising model with different exchange interactions signs and arbitrary spin values in a magnetic field. Exact analytical formulas for frustration fields, zero temperature magnetization and entropy at these fields are obtained. The general behavior of pair spin correlation function with the accounting of only interactions between nearest neighbors is examined. © 2018 The Authors, published by EDP Sciences.The reflorted study was carried out within the state assignment of FASO of Russia (theme «Quantum» n. 01201463332) and was funded by RFBR according to the research flroject n. 16-32-00032

Ordering and frustrations in generalized Ising chain

The Ising model on a one-dimensional monoatomic equidistant lattice with different nearest-neighbour and second-neighbour exchange interactions is researched. Generalized Kramers-Wannier transfer-matrix with translation on two periods of a lattice is introduced. A property similar to supercooling and superheating is detected. At the triple points phases are not individualized, but completely frustrated which corresponds to the phenomenon of critical opalescence. Exact analytical expressions for free energy, heat capacity and entropy including zero-temperature entropy are obtained. Various new special cases were analyzed and compared with all known results. All frustration fields for magnetization, frustration values for the zero-temperature entropy and magnetization are found. © Published under licence by IOP Publishing Ltd.Ural Branch, Russian Academy of Sciences, UB RAS: 18-2-2-11The research was carried out within the state assignment of Minobrnauki of Russia (theme ”Quantum” No. AAAA-A18-118020190095-4), supported in part by Ural Branch of the Russian Academy of Sciences (project No. 18-2-2-11)

GENERALIZED ISING MODEL IN A MAGNETIC FIELD

The Ising model is generalized to an arbitrary number translations of a linear chain in an external magnetic field taking into account various interactions between spins. The values of frustrating entropies and magnetizations can be expressed through the limit ratio of certain number sequences.Работа выполнена в рамках государственного задания Министерства науки и высшего образования РФ (тема «Квант», No АААА-А18-118020190095-4) и «Сплавы», No AAAA-A19-119070890020-3 и при частичной поддержке Уральского отделения Российской академии наук (проект No 18-2-2-11)

The Ferromagnetic Potts model under an external magnetic field: an exact renormalization group approach

The q-state ferromagnetic Potts model under a non-zero magnetic field coupled with the 0^th Potts state was investigated by an exact real-space renormalization group approach. The model was defined on a family of diamond hierarchical lattices of several fractal dimensions d_F. On these lattices, the renormalization group transformations became exact for such a model when a correlation coupling that singles out the 0^th Potts state was included in the Hamiltonian. The rich criticality presented by the model with q=3 and d_F=2 was fully analyzed. Apart from the Potts criticality for the zero field, an Ising-like phase transition was found whenever the system was submitted to a strong reverse magnetic field. Unusual characteristics such as cusps and dimensional reduction were observed on the critical surface.Comment: 8 pages, 6 figures. Accepted to be published in Phys. Rev B (2006