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Número de los Estados Base en Sistemas Ising 1D Linéales

S. Carpinteyro Bernardino, José Eladio Flores-Mena, J. P. Martínez-Garcilazo, E. M. Gutiérrez-Arias, María Monserrat Morín Castillo

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

We studied regular chains of one-dimensional Ising system of spin s = ½, with two types of interaction at nearest neighbors, at once we extend the analysis up to second neighbors with two types of interaction. The ground states in the diatomic model it is established exploring regular chains of blocks of spins with shorter length, named irreducible blocks. We construct the phase diagrams according to the parameters of interaction. Also there does a simulation of the decrease of the energy for random finite chains of spins, finding the regions of the configurations of lower energy of the chains.

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Orderings of one-dimensional Ising systems with an arbitrary interaction of finite range. II

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For pt. I see abstr. A11864 of 1974. A study is made of the ground state orderings of the one-dimensional Ising system, under the assumption that the interaction is of finite range r and has inversion symmetry. It is shown that the ground state energy is effected by the regular chain either of an irreducible block without or with one symmetry point of r or (r+1) sites, or of a symmetric irreducible block with two symmetry points. For the case of the one-dimensional Ising magnet under a uniform external field, it is effected by two, four, seven and twenty regular orderings, when the range r of the interaction is one, two, three and four, respectively.

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We generalize Morita's works [J. Phys. A 7, 289 (1974); J. Phys. A 7, 1613 (1974)] on ground states of Ising chains, for chains with a periodic structure and different spins, to any interaction order. The main assumption is translational invariance. The length of the irreducible blocks is a multiple of the period of the chain. If there is parity invariance, it restricts the length in general only in the diatomic case. There are degenerated states and under certain circumstances there could be nonregular ground states. We illustrate the results and give the ground state diagrams in several cases.

arXiv:1412.7423•Physical Review E•Apr 23, 2015•0 citations
We studied regular chains of one-dimensional Ising system of spin s = ½, with two types of interaction at nearest neighbors, at once we extend the analysis up to second neighbors with two types of interaction. The ground states in the diatomic model it is established exploring regular chains of blocks of spins with shorter length, named irreducible blocks. We construct the phase diagrams according to the parameters of interaction. Also there does a simulation of the decrease of the energy for random finite chains of spins, finding the regions of the configurations of lower energy of the chains.
The concept of the irreducible block is introduced for the one-dimensional Ising system with an arbitrary interaction of finite range. It is proved that the ground state energy of the system occurs for a regular chain of one of the irreducible blocks or for coexistence of the regular chains of the irreducible blocks. It is shown that the ground state energy of the linear Ising magnet with pair interactions up to third neighbours is effected by the seven spin orderings recently given for the case of spin 1 / 2 by Katsura and Narita (1973), and that the ground state energy of the Ising magnet of spin larger than 1 / 2 is effected by the same set of orderings as for the corresponding Ising magnet of spin 1 / 2 .
For pt. I see abstr. A11864 of 1974. A study is made of the ground state orderings of the one-dimensional Ising system, under the assumption that the interaction is of finite range r and has inversion symmetry. It is shown that the ground state energy is effected by the regular chain either of an irreducible block without or with one symmetry point of r or (r+1) sites, or of a symmetric irreducible block with two symmetry points. For the case of the one-dimensional Ising magnet under a uniform external field, it is effected by two, four, seven and twenty regular orderings, when the range r of the interaction is one, two, three and four, respectively.
The ground state of an Ising-type spin-1/2 chain with ferromagnetic bond-alternating nearest-neighbor and anti-ferromagnetic uniform next-nearest-neighbor interactions is studied by using the exact-diagonalization method and the density-matrix renormalization-group method. The Hamiltonian describing the system is expressed as H = – Σi h2i–1,2i – J1 Σi h2i,2i+1 + J2 Σi hi,i+2 with hi,i' = γ(Six Si'x + Siy Si'y) + Siz Si'z, where J1 0, J2 0, and 1 > γ 0. Special attention is paid to the ground-state phase diagram on the J1 versus J2 plane for a given value of γ. The phase diagram is composed of the ferromagnetic, intermediate, and up-up-down-down phases, the intermediate phase being characterized by its magnetization, which takes finite but unsaturated values. The phase diagram obtained for γ = 0.5 shows that the region of the intermediate phase for a given value of J1 is widest when J1 = 1.0 and becomes narrower rather rapidly as J1 decreases or increases from 1.0. The J2-dependence of the ground-state magnetization for γ = 0.5 and J1 = 0.85 is also discussed. PACS Nos.: 75.10Jm, 75.40Mg
The phase diagrams of the ferromagnetic two-dimensional mixed spin-1 and spin-1/2 Ising model with four-spin interaction J4 and next-nearest couplings J’ are investigated by the use of the finite cluster approximation based on single-site cluster theory. The state equations are derived for the two-dimensional square lattice. The phase diagram is qualitatively and quantitatively different from that obtained when the interaction J’ is ignored. In fact, the system exhibits a variety of interesting features resulting from the introduction of the next-nearest neighbor interaction (NNN). It undergoes two kinds of behavior according to the negative and the positive value of J’. In particular, for J4/J2=-4, the system keeps the coexistence of the two ground state up to J’-dependent finite temperature.
We study the ground state phase diagram of a two dimensional mixed-spin system of coupled alternating spin-1 and 1/2 chains with a stripe supersolid phase. Utilizing different analytical and numerical approaches such as mean field approximation, cluster mean field theory and linear spin wave theory, we demonstrate that our system displays a rich ground state phase diagram including novel stripe supersolid, solids with different fillings and super-counterfluid phases, in addition to a stripe solid with half filling, superfluid and Mott insulating phases. In order to find a minimal mixed-spin model for stripe supersolidity, in the second part of the paper we consider two kinds of mixed-spin system of coupled alternating spin-1 and 1/2 chains with (i) anisotropic nearest neighbor interactions, (ii) anisotropic hoppings and study their ground state phase diagrams. We demonstrate that, for the systems with uniform hoppings, the repulsive intra-chains interactions are necessary for stripe supersolidity. In this case the minimal two dimensional mixed-spin model is a system of spin-1 and spin-1/2 XXZ chains, interacting via Ising Hamiltonian. In the case of anisotropic hoppings, a system of coupled Ising chains is the minimal model.
We generalize Morita's works [J. Phys. A 7, 289 (1974); J. Phys. A 7, 1613 (1974)] on ground states of Ising chains, for chains with a periodic structure and different spins, to any interaction order. The main assumption is translational invariance. The length of the irreducible blocks is a multiple of the period of the chain. If there is parity invariance, it restricts the length in general only in the diatomic case. There are degenerated states and under certain circumstances there could be nonregular ground states. We illustrate the results and give the ground state diagrams in several cases.