Thermodynamic properties of the exactly solvable transverse Ising model on decorated planar lattices (original) (raw)
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Exact results of the transverse Ising model on decorated lattices
Physics Letters A, 1999
A decorated transverse Ising model on regular planar lattices is studied by the use of a generalized decoration-iteration transformation. The exact mapping relations between the singly decorated transverse Ising model and undecorated Ising Ž model without transverse field are derived. On basis of this mapping, the phase diagrams in the case of S s 1r2 S B B. denotes the spin of a decorating atom are obtained and discussed.
Physica E: Low-dimensional Systems and Nanostructures, 2018
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 decorationiteration 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 to be present at zero magnetic field. The inverse magnetocaloric effect can also be detected slightly above continuous phase transitions following the power-law dependence | − ∆S min iso | ∝ h n , where n depends basically on the ground-state spin ordering.
Phase diagram of spin-1 Ising model in a transverse crystal field
Physica A: Statistical Mechanics and its Applications, 1999
The ferromagnetic spin-1 Ising model with a transverse crystal ÿeld is studied within the framework of the e ective ÿeld theory on honeycomb, square and cubic lattices. We have investigated the e ect of the transverse crystal ÿeld on the magnetization and quadrupolar moments, and phase diagrams of the system. The tricritical phenomena has not been observed in our system.
Acta Physica Polonica A, 2017
Magnetocaloric properties of the spin-1/2 Ising model on a decorated square lattice in a transverse magnetic field are investigated by the use of a generalized decoration-iteration transformation, which establishes a rigorous mapping correspondence with the zero-field spin-1/2 Ising model on a square lattice. The temperature dependence of the entropy, the isothermal entropy change and the adiabatic temperature change display anomalous singular behavior in a vicinity of a second-order phase transition. The large inverse magnetocaloric effect can be found in the isothermal entropy change within the temperature interval, which is delimited by the critical temperatures at zero and non-zero transverse fields.
Physica A-statistical Mechanics and Its Applications - PHYSICA A, 2004
The transverse spin-1 Ising model with a longitudinal crystal field presents a rich variety of critical phenomena. Using the effective field theory with a probability distribution technique that accounts for the self-spin correlation functions, the phase diagrams and the tricritical points are investigated for the square lattice (N=4). The results show that the tricritical points exist for certain values of the strength of the transverse field and the strength of the longitudinal crystal field. The longitudinal and the transverse magnetizations as well as the longitudinal and the transverse quadrupolar moments are also examined. These quantities as functions of the temperature, the strength of the longitudinal crystal field and the strength of the applied transverse field are calculated numerically and some interesting results are obtained.
Thermodynamic properties of the triangular-lattice ising antiferromagnet in a uniform magnetic field
Using both the exact enumeration method (microcanonical transfer matrix) for small systems (up to 9 ¢ 9 lattices) and the Wang-Landau Monte Carlo algorithm for large systems (up to 30 ¢ 30 lattices), we obtain the exact and approximate densities of states g(M; E), as a function of magnetization M and exchange energy E, for the triangular-lattice Ising model in the presence of an external uniform magnetic eld. The method for evaluating the exact density of states g(M; E) of the triangular-lattice Ising model is introduced for the rst time. Based on the density of states g(M; E), we investigate the properties of the various thermodynamic quantities as a function of temperature T and magnetic eld h and nd the phase diagram of the Ising antiferromagnet in the magnetic eld. In addition, the zero-temperature thermodynamic properties are studied by reference to the density of states at the corner or along the edge line on the magnetization-energy (ME) diagram.
Phase diagrams and tricritical behavior in a spin- Ising model with transverse crystal field
Physica A: Statistical Mechanics and its Applications, 2002
Within the framework of the e ective-ÿeld theory with correlations, the ferromagnetism of spin-3 2 Ising model with a transverse crystal ÿeld on honeycomb and square and simple cubic lattices is studied. Tricritical phenomena have been observed for the square and simple cubic lattices, but there is no tricritical point for the honeycomb lattice. We have investigated the e ect of the transverse crystal ÿeld on the phase diagrams, magnetization, quadrupolar moments, internal energy, and speciÿc heat of the system on the square lattice in detail.
Journal of Magnetism and Magnetic Materials, 2010
A spin-1 transverse Ising model with longitudinal crystal field in a longitudinal magnetic field is examined by introducing an effective field approximation (IEFT) which includes the correlations between different spins that emerge when expanding the identities. The effects of the crystal field as well as the transverse and longitudinal magnetic fields on the thermal and magnetic properties of the spin system are discussed in detail. The order parameters, Helmholtz free energy and entropy curves are calculated numerically as functions of the temperature and Hamiltonian parameters. A number of interesting phenomena such as reentrant phenomena originating from the temperature, crystal field, transverse and longitudinal magnetic fields have been found.
arXiv (Cornell University), 2002
Magnetic properties of the 1D mixed spin-1/2 and spinS (S >1/2) transverse Ising model in the presence of an external longitudinal magnetic field are calculated exactly by the use of the generalised decoration-iteration mapping transformation. By assuming that only the spinS atoms do interact with the transverse field the exact results for the Gibbs free energy, longitudinal magnetization, transverse magnetization, entropy and specific heat have been derived and discussed in detail. In addition to the standard temperature variations of the transverse magnetization, another two non-trivial thermal dependences have been found. The results support the concept that the spin reorientation from the longitudinal towards the transverse field direction takes place in the narrow temperature region.
Physics Letters A, 2012
The spin-1/2 Ising model with a spin-phonon coupling on decorated planar lattices partially amenable to lattice vibrations is examined within the framework of the generalized decoration-iteration transformation and the harmonic approximation. It is shown that the magnetoelastic coupling gives rise to an effective antiferromagnetic next-nearestneighbour interaction, which competes with the nearest-neighbour interaction and is responsible for a frustration of the decorating spins. The strong enough spin-phonon coupling consequently leads to an appearance of the striking partially ordered and partially disordered phase, where a perfect antiferromagnetic alignment of the nodal spins is accompanied with a complete disorder of the decorating spins. The diversity in temperature dependences of the total specific heat is investigated in connection with the particular behaviour of its magnetic and lattice contribution.