The magnetocaloric properties of the Ising binary alloys composed of arbitrary spin values, have been determined by using effective field theory. For determining the efficiency of the magnetocaloric effect in binary alloy, the quantities of interest such as isothermal magnetic entropy change and refrigerant capacity have been calculated for various values of spin and concentration. It is shown that, by changing the concentration we can tune the magnetocaloric performance. Also, it has been shown that greater refrigerant capacity can be obtained for intermediate concentration values, in comparison with the limiting concentration values.
The symmetric spin-1/2 Ising-Heisenberg diamond chain with different Landé g-factors of Ising and Heisenberg spins is exactly solved by combining the generalized decoration-iteration transformation and transfer-matrix method. The ground state of the system and magnetocaloric effect during the adiabatic (de)magnetization are particularly examined. It is evidenced that the considered mixed-spin diamond chain exhibits an enhanced magnetocaloric effect during the adiabatic (de)magnetization in the vicinity of field-induced phase transitions as well as in the zero-field limit if the frustrated phas…
Magnetization process and adiabatic demagnetization of the antiferromagnetic Ising spin clusters with the shape of regular polyhedra (Platonic solids) are exactly examined within the framework of a simple graph-theoretical approach. While the Ising cube as the only unfrustrated (bipartite) spin cluster shows just one trivial plateau at zero magnetization, the other regular Ising polyhedra (tetrahedron, octahedron, icosahedron and dodecahedron) additionally display either one or two intermediate plateaux at fractional values of the saturation magnetization. The nature of highly degenerate groun…
The magneticaloric properties of the Ising nanotube constituted by arbitrary core spin values $S_c$ and the shell spin values $S_s$ have been investigated by mean field approximation. During this investigation, several quantities have been calculated, such as isothermal magnetic entropy change, full width at half maximum value and the refrigerant capacity. The variation of these quantities with the values of the spins and exchange interaction between the core and shell is determined. Besides, recently experimentally observed double peak behavior in the variation of the isothermal magnetic entr…
The ground-state degeneracy and magnetocaloric effect in the spin-$1/2$ Ising-Heisenberg double-tetrahedral chain are exactly investigated. It is demonstrated that the zero-temperature phase diagram involves two classical and two quantum chiral phases with distinct degrees of the macroscopic degeneracy. Different macroscopic degeneracies observed in the latter phases and at individual ground-state phase transitions are confirmed by multiple-peak dependencies of the specific heat and entropy on the magnetic field. The cooling capability of the model is well illustrated by the magnetic-field var…
The ground state, zero-temperature magnetization process, critical behaviour and isothermal entropy change of the mixed-spin Ising model on a decorated triangular lattice in a magnetic field are exactly studied after performing the generalized decoration-iteration mapping transformation. It is shown that both the inverse and conventional magnetocaloric effect can be found near the absolute zero temperature. The former phenomenon can be found in a vicinity of the discontinuous phase transitions and their crossing, while the latter one occurs in some paramagnetic phases due to a spin frustration…
The isothermal magnetic entropy change has been obtained for the bilayer system that consists of $S_u$ and $S_l$ valued spins in each layer. The relation between the IMEC and the spin value as well as the value of exchange interaction between two layers have been obtained. Recently experimentally given double peaks behavior for manganite bilayers has been demonstrated theoretically, and explanation is given. On the other hand, the conditions that give rise to transition from this double peak behavior to the single peak behavior have been obtained and discussed.
Magnetocaloric effect in a double-tetrahedral chain, in which nodal lattice sites occupied by the localized Ising spins regularly alternate with three equivalent lattice sites available for mobile electrons, is exactly investigated by considering the one-third electron filling and the ferromagnetic Ising exchange interaction between the mobile electrons and their nearest Ising neighbours. The entropy and the magnetic Gruneisen parameter, which closely relate to the magnetocaloric effect, are exactly calculated in order to investigate the relation between the ground-state degeneracy and the coo…
Magnetic and magnetocaloric properties of geometrically frustrated antiferromagnetic Ising (IA) and ferromagnetic spin ice (SI) models on a nanocluster with a `Star of David' topology, including next-nearest-neighbor (NNN) interactions, are studied by an exact enumeration. In an external field applied in characteristic directions of the respective models, depending on the NNN interaction sign and magnitude, the ground state magnetization of the IA model is found to display up to three intermediate plateaus at fractional values of the saturation magnetization, while the SI model shows only one …
Owing to a high degree of geometrical frustration an Ising antiferromagnet on a kagome lattice (IAKL) is known to exhibit no long-range ordering at any temperature, including the ground state. Nevertheless, at low temperatures it shows a strongly correlated, highly fluctuating regime known as a cooperative paramagnet or classical spin liquid. In the ground state it is characterized by a macroscopic degeneracy which translates to a relatively large value of the residual entropy. It has been shown that the presence of a macroscopic degeneracy associated with geometrical frustration below the sat…
The entropy and cooling rate of the both antiferromagnetic spin-1/2 double sawtooth IsingHeisenberg model and mixed-spin (1,1/2) double sawtooth Ising-Heisenberg model on the distorted ladders are rigorously investigated under an adiabatic demagnetization process using the quantum transfer-matrix technique. The models include the XXZ interaction between the interstitial Heisenberg dimers, the Ising coupling between nearest-neighbor spins of the legs and rungs, and additional cyclic four-spin exchange (ring exchange) in the square plaquette of each block. Close to field-induced quantum phase tr…
Effects of a single-ion anisotropy on magnetocaloric properties of selected spin-$s\geq 1$ antiferromagnetic Ising clusters with frustration-inducing triangular geometry are studied by exact enumeration. It is found that inclusion of the single-ion anisotropy parameter $D$ can result in a much more complex ground-state behavior, which is also reflected in a magnetocaloric effect (MCE) at finite temperatures. For negative $D$ (easy-plane anisotropy) with increasing $s$ the ground-state magnetization as a function of the external field gradually shows increasing number of plateaus of various hei…
The magnetic and magnetocaloric properties of the mixed spin-(1/2,1) Ising-Heisenberg model on a two-leg ladder with dimer-rung alternation are exactly examined under an adiabatic demagnetization process using the transfer-matrix formalism. We notify that the magnetization curve of the model exhibits plateaux as a function of the applied magnetic field and cyclic four-spin Ising interaction at certain rational fractions of the saturation value. We precisely investigate the ability of cooling/heating of the model nearby the critical points at which discontinuous ground-state phase transition oc…
Ground-state and magnetocaloric properties of a double-tetrahedral chain, in which nodal lattice sites occupied by the localized Ising spins regularly alternate with triangular clusters half filled with mobile electrons, are exactly investigated by using the transfer-matrix method in combination with the construction of the $N$th tensor power of the discrete Fourier transformation. It is shown that the ground state of the model is formed by two non-chiral phases with the zero residual entropy and two chiral phases with the finite residual entropy $S = Nk_{\rm B}\ln 2$. Depending on the charact…
A spin-1/2, Ising trilayered ferrimagnetic system on square Bravais lattice is studied, employing Monte-Carlo simulation with the single spin-flip Metropolis algorithm. The bulk of such a system is formed by three layers, each of which is composed entirely either by A or B type of atoms, resulting in two distinct compositions: ABA and AAB and two different types of magnetic interactions: ferromagnetic between like atoms and antiferromagnetic between unlike atoms. For such systems, Inverse Absolute of Reduced Residual Magnetisation is the absolute value of the ratio of the extremum of the magne…
The spin-1/2 Ising octahedron and dodecahedron with a unique antiferromagnetic interaction display an outstanding magnetization jump at zero magnetic field, which consequently leads to a giant magnetocaloric effect during the adiabatic demagnetization. In the present work we report temperature dependences of two basic magnetocaloric response functions: the isothermal entropy change and the adiabatic change of temperature. It is shown that the Ising octahedron and dodecahedron generally exhibit a large negative isothermal entropy change upon increasing of the magnetic field, which serves in evi…
The magnetization curves and magnetocaloric effect during the adiabatic demagnetization of antiferromagnetic spin-1/2 $XXZ$ Heisenberg clusters with the shape of Johnson's solids (triangular cupola, square cupola and pentagonal cupola) are investigated using the exact numerical diagonalization for different values of the exchange anisotropy ranging in between the Ising and fully isotropic limit. It is demonstrated that spin-1/2 $XXZ$ Heisenberg cupolae display, in comparison with their Ising counterparts, at least one more magnetization plateau. The novel magnetization plateaux extends over a …
Magnetic properties of the spin-1/2 XXZ Heisenberg cuboctahedron are examined using exact numerical diagonalization depending on a relative strength of the exchange anisotropy. While the Ising cuboctahedron exhibits in a low-temperature magnetization curve only one-third magnetization plateau, the XXZ Heisenberg cuboctahedron displays another four intermediate plateaux at zero, one-sixth, one-half and two-thirds of the saturation magnetization. The novel magnetization plateaux generally extend over a wider range of magnetic fields with increasing of a quantum ($xy$) part of the XXZ exchange in…
Magnetization plateaus and enhanced magnetocaloric effect of a spin-1/2 Ising-Heisenberg and Heisenberg double sawtooth ladder with four-spin interaction
The magnetization process and adiabatic demagnetization of the antiferromagnetic spin-1/2 XXZ Heisenberg clusters with the shape of regular polyhedra (tetrahedron, octahedron, cube, icosahedron and dodecahedron) are examined using the exact diagonalization method. It is demonstrated that a quantum (xy) part of the XXZ exchange interaction is a primary cause for presence of additional intermediate magnetization plateaux and steps, which are totally absent in the limiting Ising case. The only exception to this rule is the spin-1/2 XXZ Heisenberg tetrahedron, which shows just a quantitative shift…
Magnetization, entropy and magnetocaloric properties of various geometrically frustrated tetrahedra-based Ising antiferromagnetic nanoclusters with corner-, edge-, and face-sharing topologies are studied by exact enumeration. It is found that the studied properties strongly depend on the nanocluster topology and can be very different from those of a single tetrahedron as well as the pyrochlore lattice formed by an infinite number of corner-sharing tetrahedra. From the magnetocaloric point of view an important difference from the latter two systems is the absence of the ground-state zero-magnet…
Hysteresis behaviors of the binary alloy system represented by the formula $A_c B_{1-c}$ have been investigated within the framework of EFT. The system consists of type A atoms (spin-$1$) with concentration $c$ and type B atoms (spin-$1/2$) with concentration $1-c$. After giving the phase diagrams, we focused on the different type of hysteresis behaviors in the system. Especially, the mechanisms giving rise to double hysteresis behavior have been explained, which appear at large negative values of the crystal field and low temperatures. It has been observed that binary alloy system could exhib…
An exactly solvable spin-electron tetrahedral chain, where the Ising spins localized at nodal lattice sites regularly alternate with three equivalent lattice sites available for one mobile electron is considered. The system with ferromagnetic interaction between the Ising spins and electrons exhibits an enhanced magnetocaloric effect (MCE) in the limit $H/|J|\to 0$ when the entropy is very small, whereas the system with antiferromagnetic interaction between the Ising spins and electrons exhibits an enhanced MCE around the field $H/J=1$ when the entropy is sufficiently close to the value $S/2N …
Exploiting the mapping between a binary mixture and the Ising model we have analyzed the critical fluctuations by means of the density-matrix renormalization group technique. The calculations have been carried out for a two-dimensional Ising strip subject to equal strong surface fields. It was found that the critical Casimir force displays significantly different behavior on opposite sides of the capillary condensation line, especially below the critical temperature. It can be concluded that in a real binary mixtures the most attractive force appears at temperatures near T_C and at reservoir c…
Dynamical structure factor (S(k,$ω$)) is calculated for the one-dimensional (1D) transverse field Ising model, and its recent extension to include a three spin term, with quenched binary disorder. We study the low energy modes for lattices as large as 256 sites. We show that the intense zero energy modes appear whenever the binary disorder straddles two different winding numbers. We argue that these are Majorana modes, which reside on the boundaries of the rare regions. The size distribution of Majorana pairs has a fractal behavior at the critical points. With the longer ranged interactions a …
In the many fields in which the Ising model is applied nowadays, the spin variables are often assumed to be of spin-class $\{-1,1\}$ or $\{0,1\}$, even though for any mix of binary real valued spin-classes a proper Ising model distribution exists. Here we show that in their basis all these spin-classes are the same, as a simple expressions exist that allow us to transform the variables from one particular mix of spin-classes to any other combination, without changing the probabilities for the system states as a whole.
Effects of dynamical activity spillover in a noisy binary choice game (Ising game) on a complete graph are studied. Binary choice games are very important for both economics and statistical physics playing a role of the bridge between these two fields. In this paper we investigate the effects of self-excited activity induced by activity spillover on relaxation to equilibria and transitions between metastable equilibria at finite times. Using the formalism of master equations we show that both relaxation and interequilibria transitions at finite time are accelerated by the effects of activity s…
Binary random variables are the building blocks used to describe a large variety of systems, from magnetic spins to financial time series and neuron activity. In Statistical Physics the Kinetic Ising Model has been introduced to describe the dynamics of the magnetic moments of a spin lattice, while in time series analysis discrete autoregressive processes have been designed to capture the multivariate dependence structure across binary time series. In this article we provide a rigorous proof of the equivalence between the two models in the range of a unique and invertible map unambiguously lin…
Geometric Characteristics of Subproblems in Ising-Machine-Assisted Large Neighborhood Search
Graduate School of Science and Technology, Keio University（庆应义塾大学理工学部研究生科）；Department of Applied Physics and Physico-Informatics, Keio University（庆应义塾大学应用物理及物理信息学系）；Keio University Sustainable Quantum Artificial Intelligence Center (KSQAIC), Keio University（庆应义塾大学可持续量子人工智能中心）；Human Biology-Microbiome-Quantum Research Center (WPI-Bio2Q), Keio University（庆应义塾大学生物微生物组量子研究中心）；Green Computing System Research Organization, Waseda University（早稻田大学绿色计算系统研究组织）
Black-box optimization using factorization and Ising machines
National Institute for Materials Science（物质材料研究机构）；Graduate School of Frontier Sciences, The University of Tokyo（东京大学前沿科学研究生院）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）；Graduate School of Science and Technology, Keio University（庆应义塾大学理工学研究科）；Fixstars Amplify Corporation（Fixstars Amplify公司）；Unprecedented-scale Data Analytics Center, Tohoku University（东北大学超大规模数据分析中心）；Fixstars Corporation（Fixstars公司）；Department of Applied Physics and Physico-Informatics, Keio University（庆应义塾大学应用物理与物理信息学系）；Keio University Sustainable Quantum Artificial Intelligence Center (KSQAIC)（庆应义塾大学可持续量子人工智能中心）；Human Biology-Microbiome-Quantum Research Center (WPI-Bio2Q), Keio University（庆应义塾大学人类生物学-微生物组-量子研究中心）
We find an exact mapping from the generalized Ising models with many-spin interactions to equivalent Boltzmann machines, i.e., the models with only two-spin interactions between physical and auxiliary binary variables accompanied by local external fields. More precisely, the appropriate combination of the algebraic transformations, namely the star-triangle and decoration-iteration transformations, allows one to express the model in terms of fewer-spin interactions at the expense of the degrees of freedom. Furthermore, the benefit of the mapping in Monte Carlo simulations is discussed. In parti…
Motivated by efforts to create thin nanoscale metamaterials and understand atomically thin binary monolayers, we study the finite temperature statistical mechanics of arrays of bistable buckled dilations embedded in free-standing two-dimensional crystalline membranes that are allowed to fluctuate in three dimensions. The buckled nodes behave like discrete, but highly compressible, Ising spins, leading to a phase transition at $T_c$ with singularities in the staggered "magnetization," susceptibility, and specific heat, studied via molecular dynamics simulations. Unlike conventional Ising models…
