Ising Model In Magnetic Field Research Articles

Corner transfer matrix approach to the Yang-Lee singularity in the two-dimensional Ising model in a magnetic field.

We study the two-dimensional (2D) Ising model in a complex magnetic field in the vicinity of the Yang-Lee edge singularity. By using Baxter's variational corner transfer matrix method combined with analytic techniques, we numerically calculate the scaling function and obtain an accurate estimate of the location of the Yang-Lee singularity. The existing series expansions for susceptibility of the 2D Ising model on a triangular lattice by Chan, Guttmann, Nickel, and Perk allowed us to substantially enhance the accuracy of our calculations. Our results are in excellent agreement with the Ising field theory calculations by Fonseca, Zamolodchikov, and the recent work by Xu and Zamolodchikov. In particular, we numerically confirm an agreement between the leading singular behavior of the scaling function and the predictions of the M_{2/5} conformal field theory.

Specific-Heat Anomaly of the Kagomé-Lattice Ising Model in a Magnetic Field

The properties of the kagome-lattice Ising model in an external magnetic field B have not been known well. The specific-heat anomaly of the kagome-lattice Ising model in an external magnetic field is investigated based on the enthalpy fluctuation. As the magnetic field increases, the specific heat maximum decreases, but it approaches non-zero value for large magnetic field. In particular, the asymptotic line to the specific-heat maximum temperature Th(B) follows Th(B) = 0.8335565596(B + 4). The well-known experimentalist formula Tp(B) = 0.8335565596B for paramagnet shows the same slope as the asymptotic line Th (B) of the kagome-lattice Ising model in an external magnetic field.

Design of geometric phase gates and controlling the dynamic phase for a two-qubit Ising model in magnetic fields

We investigate how to obtain a non-trivial geometric phase gate for a two-qubit spin chain, with Ising interaction in different magnetic fields. Indeed, one of the spins is driven by a time-varying rotating magnetic field, and the other is coupled with a static magnetic field in the direction of the rotation axis. This is an interesting problem both for the purpose of measuring the geometric phases and in quantum computing applications. It is shown that the static magnetic field does not change the adiabatic states of the system, and it does not affect the geometric phases, whereas it may be used to control the dynamic phases. In addition, by considering the exact two-spin adiabatic geometric phases, we find that a non-trivial two-spin unitary transformation, purely based on Berry phases, can be obtained by using two consecutive cycles with opposite directions of the magnetic fields, opposite signs of the interaction constant and the phase shift of the rotating magnetic field. In addition, in the non-adiabatic case, starting with a certain initial state, a cycle can be achieved and thus the Aharonov–Anandan phase is calculated.

Tomonaga–Luttinger Liquid in Quasi-One-Dimensional Antiferromagnet BaCo2V2O8in Magnetic Fields

Motivated by recent studies on the quasi-one-dimensional (1D) antiferromagnet BaCo 2 V 2 O 8 , we investigate the Tomonaga–Luttinger-liquid properties of the 1D S =1/2 X X Z Heisenberg–Ising model in magnetic fields. By using the Bethe ansatz solution, thermodynamic quantities and the divergence exponent of the NMR relaxation rate are calculated. We observe a magnetization minimum as a function of temperature ( T ) close to the critical field. As the magnetic field approaches the critical field, the minimum temperature asymptotically approaches the universal relation in agreement with the recent results by Maeda et al. We observe T -linear specific heat below the temperature of the magnetization minimum. The field dependence of its coefficient agrees with the results based on conformal field theory. The field dependence of the divergence exponent of the NMR relaxation rate with decreasing temperature is obtained, indicating a change in the critical properties. The results are discussed in connection with ...

Exact solution of the one-dimensional spin- $\frac{\mathsf 3}{\mathsf 2}$ Ising model in magnetic field

In this paper, we study the Ising model with general spin $S$ in presence of an external magnetic field by means of the equations of motion method and of the Green's function formalism. First, the model is shown to be isomorphic to a fermionic one constituted of $2S$ species of localized particles interacting via an intersite Coulomb interaction. Then, an exact solution is found, for any dimension, in terms of a finite, complete set of eigenoperators of the latter Hamiltonian and of the corresponding eigenenergies. This explicit knowledge makes possible writing exact expressions for the corresponding Green's function and correlation functions, which turn out to depend on a finite set of parameters to be self-consistently determined. Finally, we present an original procedure, based on algebraic constraints, to exactly fix these latter parameters in the case of dimension 1 and spin $\frac32$. For this latter case and, just for comparison, for the cases of dimension 1 and spin $\frac12$ [F. Mancini, Eur. Phys. J. B \textbf{45}, 497 (2005)] and spin 1 [F. Mancini, Eur. Phys. J. B \textbf{47}, 527 (2005)], relevant properties such as magnetization $<S>$ and square magnetic moment $<S^2 >$, susceptibility and specific heat are reported as functions of temperature and external magnetic field both for ferromagnetic and antiferromagnetic couplings. It is worth noticing the use we made of composite operators describing occupation transitions among the 3 species of localized particles and the related study of single, double and triple occupancy per site.

Exactly solvable weak-graph duals of a generalized ising model on the Kagome lattice

We recover the known and find some nontrivial new "exactly solvable" subspaces in the parameter space of a generalized Ising model in magnetic field formulated on the Kagome lattice.

PHASE BOUNDARY AND UNIVERSALITY OF THE TRIANGULAR LATTICE ANTIFERROMAGNETIC ISING MODEL

Transfer matrix methods are used to locate accurate phase boundary of the triangular lattice antiferromagnetic Ising model in magnetic field. Universal quantities such as the central charge and the first few scaling dimensions are obtained along the phase boundary except near the zero field point where the crossover effect degrades convergence. Numerical results are fully consistent with the operator content of the 3-state Potts model indicating that whole phase boundary belongs to the 3-state Potts universality class.

Critical line of the square-lattice antiferromagnetic Ising model in a magnetic field

A closed-form expression is proposed for the critical line of the antiferromagnetic Ising model in a nonzero magnetic field on the square lattice. The proposed expression reproduces all known numerical data to a high degree of accuracy.

Thue-Morse quantum Ising model.

We study the one-dimensional quantum Ising model in a transverse magnetic field where the exchange couplings are ordered according to the Thue-Morse (TM) sequence. At zero temperature, this model is equivalent to a two-dimensional classical Ising model in a magnetic field with TM aperiodicity along one direction. We compute the order parameter (magnetization) of the chain and the scaling behavior of the energy spectrum when the system undergoes a phase transition. Analogous to the quasiperiodic (QP) quantum Ising chain, the onset of long-range order is signaled by a nonanaliticity in the exponent delta which describes the scaling of the total bandwidth with the size of the chain. The critical spin-coupling can be computed analytically and it is found to be lower than the QP case. Furthermore, the energy bands are found to be narrower than the corresponding QP chain. The former and latter results are consistent with the fact that the present structure has a degree of ordering intermediate between QP and random.

Isostructural phase transitions in solids

A model of electrons interacting with lattice vibrations is shown to exhibit an isostructural phase transition as a function of applied force by relating the Hamiltonian to that of an Ising model in magnetic field.

On the solution of the two-dimensional ising model with an imaginary magnetic field βH=h=iπ/2

The aim of this note is to give a simple and direct proof of the Lee-Yang expression for the solution of the two-dimensional Ising model at exp [-2h] = z = 1, which corresponds to a pure imaginary magnetic field equal to in~2 = h = f iB , fl = ( k T ) L We briefly recall the history of this particular problem in the following way. In one of the two fundamental papers celebrating the circle theorem and the spontaneous magnetization of the Ising model (~) the solution of the Ising model in magnetic field at the point z = 1 was announced. As was pointed out later by BAXTER (2), LEE and YX-~G never gave explicitly the proof of their result for this particular problem, but in (~) it was noted that the solution could be obtained by an extension of the method due to Kxc and WARD for the case z,=, 1 ( h = 0 ) . In a second step (2.3), BXXTER derived the Lee-Yang formula for the free-energy density using the combinatorial approach. This was a consequence of a strong analysis of the group structure which can be used to characterize global properties such as area in the Ising model with magnetic field. In fact, BAXTER introduced a system of weights, which, for any closed path, gives, in addition to (2n) -~ time, the change in the argument of the tangent vector (modulo 2), the number of enclosed units of area (modulo 2) corresponding to z = 1. Nevertheless, in the first step of his proof, BAXTER used an extension of the Sherman theorem on path (z = 1) (as), but no explicit proof was given about validity of this extension for z = 1. In this context, we think therefore, that it is interesting to give another more simple and direct proof of the Yang-Lee fornmla, as an application of another concept of path described by KADANOFF and CEVA (e) and used for the duality transformation of correlations (7). In a second step we make use of the result of UTIYAMA for the generalized anisotropic Ising model on a square latt ice in zero field.