One-Dimensional Ising Model with General Spin

Suzuki, Masuo; Tsujiyama, Bunjiro; Katsura, Seiichiro

doi:10.1063/1.1705089

Cited by 96 publications

(21 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The grand partition function (2.4) with the (asymptotic) A m from Table 5 and the solutions (4.9), (4.10) becomes 11) in agreement with the transfer-matrix result for the canonical partition function Z N [5], where the factor e KN again originates from a shift in energy scale. For the average numbers of soliton pairs, N m , we must solve six linear equations of the type (2.6) with the w m from (4.9), (4.10).…”

Section: Statistical Mechanics Of Soliton Pairssupporting

confidence: 70%

See 1 more Smart Citation

Statistically interacting quasiparticles in Ising chains

Vanasse

Piecuch

et al. 2008

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

Abstract. The exclusion statistics of two complementary sets of quasiparticles, generated from opposite ends of the spectrum, are identified for Ising chains with spin s = 1/2, 1. In the s = 1/2 case the two sets are antiferromagnetic domain walls (solitons) and ferromagnetic domains (strings). In the s = 1 case they are soliton pairs and nested strings, respectively. The Ising model is equivalent to a system of two species of solitons for s = 1/2 and to a system of six species of soliton pairs for s = 1. Solitons exist on single bonds but soliton pairs may be spread across many bonds. The thermodynamics of a system of domains spanning up to M lattice sites is amenable to exact analysis and shown to become equivalent, in the limit M → ∞, to the thermodynamics of the s = 1/2 Ising chain. A relation is presented between the solitons in the Ising limit and the spinons in the XX limit of the s = 1/2 XXZ chain.

show abstract

Section: Statistical Mechanics Of Soliton Pairssupporting

confidence: 70%

“…This model system has simple product eigenstates, a dispersionless spectrum, and no intrinsic dynamics to speak of. Its thermodynamics, derived via transfer matrix [4,5], is predictably simple.…”

Section: Introductionmentioning

confidence: 99%

Statistically interacting quasiparticles in Ising chains

Vanasse

Piecuch

et al. 2008

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…in 10,12,[18][19][20]22 ). At the same time, the analysis of the conventional 1D Ising model also continues taking into account higher spin S values 24 , two kinds of spins 25 , the random short-and long-range interactions 26,27 , the next-nearest-neighbour coupling 28 and the magnetic field [29][30][31] .…”

Section: Introductionmentioning

confidence: 99%

Local distributions of the 1D dilute Ising model

Panov

2020

Journal of Magnetism and Magnetic Materials

View full text Add to dashboard Cite

The local distributions of the one-dimensional dilute annealed Ising model with charged impurities are studied. Explicit expressions are obtained for the pair distribution functions and correlation lengths, and their low-temperature asymptotic behavior is explored depending on the concentration of impurities. For a more detailed consideration of the ordering processes, we study local distributions. Based on the Markov property of the dilute Ising chain, we obtain an explicit expression for the probability of any finite sequence and find a geometric probability distribution for the lengths of sequences consisting of repeating blocks. An analysis of distributions shows that the critical behavior of the spin correlation length is defined by ferromagnetic or antiferromagnetic sequences, while the critical behavior of the impurity correlation length is defined by the sequences of impurities or by the charge-ordered sequences. For the dilute Ising chain, there are no other repeating sequences whose mean length diverges at zero temperature. While both the spin correlation and the impurity correlation lengths can diverge only at zero temperature, the ordering processes result in a maximum of the specific heat at finite temperature defined by the maximum rate of change of the impurity-spin pairs concentration. A simple approximate equation is found for this temperature. We show that the non-ordered dilute Ising chains correspond to the regular Markov chains, while various orderings generate the irregular Markov chains of different types.

show abstract

“…There is a large and diffused interest in the study of this model, motivated by several reasons. The BEG model was originally introduced to describe the phase separation and superfluidity in the 3 He- 4 He mixtures, but it can also describe the properties of a variety of systems ranging from spin-1 magnets to liquid crystal mixtures, microemulsions, semiconductor alloys, to quote a few. Both the BEG and BC models have been investigated using many different approaches for different lattice type and dimensions.…”

Section: Introductionmentioning

confidence: 99%

Magnetic and thermal properties of a one-dimensional spin-1 model

Mancini¹

2008

Condens. Matter Phys.

View full text Add to dashboard Cite

We study the one-dimensional S=1 Blume-Emery-Griffiths model. Upon transforming the spin model into an equivalent fermionic model, we provide the exact solution within the Green's function and equations of motion formalism. We show that the relevant response functions as well as thermodynamic quantities can be determined, in the whole parameters space, in terms of a finite set of local correlators. Furthermore, considering the case of an antiferromagnetic chain with single-ion anisotropy in the presence of an external magnetic field, we find three plateaus in the magnetization curve. In the neighborhood of the endpoints of the intermediate plateau, the specific heat shows a double peak structure

show abstract

One-Dimensional Ising Model with General Spin

Cited by 96 publications

References 7 publications

Statistically interacting quasiparticles in Ising chains

Statistically interacting quasiparticles in Ising chains

Local distributions of the 1D dilute Ising model

Magnetic and thermal properties of a one-dimensional spin-1 model

Contact Info

Product

Resources

About