Hidetsugu Kitatani

The verticality of the ferromagnetic-spin glass phase boundary of the ±J Ising model in the p-T plane

Assuming an appropriate condition, the verticality of the ferromagnetic-spin glass phase boundary of the ± J Ising model in the p - T plane ( p is the concentration of + J bonds: T is the temperature) has been proved rigorously, where the lattice structure containing the dimension of the lattice and the range of the interactions are arbitrary. Further, the existence of a spin glass phase in the p - T plane has been proved for a class of the ± J Ising models (which are defined in this paper) without any assumption.

Spin wave theory for a frustrated antiferromagnetic Heisenberg model on a square lattice

A spin wave theory for a frustrated antiferromagnetic Heisenberg model on a square lattice is developed using spin operators introduced by Oguchi and Honma. Exchange integrals between nearest neighbor and next nearest neighbor are denoted by J 1 = p J and J 2 =(1- p ) J where 0≤ p ≤1, and J is a positive constant. Since the ground state for 0≤ p ≤1/3 is different from that for 1/3≤ p ≤1, they are treated separately. The energy, staggered magnetization and correlation functions in the ground state are calculated over the whole range of p . For the special case of p =0, they are compared with Takahashis theory. Furthermore, direct calculations for finite lattice with 16 and 20 spins are shown for reference.

Reentrant Phenomena in Some Ising Spin Systems–Rigorous Results and Effects of an External Field–

The relation between reentrant phenomena and the ground state degeneracy due to competing interactions has been investigated by an exact investigation of the singularity of the free energy in some two-dimensional Ising models with competing periodic nearest neighbour interactions. Thermodynamic properties, in particular, magnetic properties of the system have been studied, which are shown to have similarities to some experimental results on spin glass phenomena.

Coherent-Anomaly Method Applied to the Quantum Heisenberg Model

The coherent-anomaly method proposed by M. Suzuki is applied to the spin 1/2 ferromagnetic Heisenberg model to estimate the critical exponents. The effective Hamiltonian method to small-sized clusters for the simple cubic lattice, and the inverse temperature power series expansion of the susceptibility for the face centered cubic lattice are combined with the CAM. Both results show that the CAM is useful for the quantum spin systems.

Non-Universal Critical Behavior in the Ferromagnetic Transition of the ± J Ising Model

Ferromagnetic (FM) transition of the ± J Ising model is studied for square and simple-cubic lattices by Monte Carlo simulations. Non-equilibrium relaxation (NER) process of magnetization from the all-aligned spin state is analyzed. The transition temperature is estimated at several values of FM bond concentrations to provide the boundary of the FM phase. The estimated NER exponent of magnetization shows non-universal behavior and it becomes larger smoothly when the transition temperature becomes higher.

Ferromagnetic Transition of ± J Ising Spin Glass Model on Square Lattice

The ferromagnetic transition of ± J -Ising spin-glass model on square lattice is studied by using Monte Carlo simulation. At ferromagnetic-bond density p =0.96 where the system shows ferromagnetic transition, the spontaneous magnetization, the ratio / 2 and the non-equilibrium relaxation (NER) are studied. The transition is estimated to be at K c =0.5100 (1). The analysis by NER gives the most reliable estimation with the least CPU time for simulations among the three methods. The value of magnetization exponent β is estimated to be 0.130(10) which coincides with that of the purely ferromagnetic Ising model ( p =1). The dynamical critical exponent z is estimated to be 2.418(23) from the NER analysis which is different from that of the pure model. The size of simulated lattices is up to 2001×2000, and the number of totally updated Ising spins is 5.5×10 15 .

Theory of the Resonating Valence Bond in Quantum Spin System

The theory of the resonating valence bond (RVB) for the antiferromagnetic Heisenberg model of spin 1/2 proposed by Anderson is generalized by taking account of singlet bonds connecting distant spins, and is solved exactly for the finite lattice. It is shown that the RVB wave function is S tot (total spin quantum number)=0, and that replacing a part of singlet bonds by triplet bonds, eigenfunctions with S tot =1, 2, … can be constructed. These are the new representation of eigenfunctions of the Heisenberg Hamiltonian.

Ferromagnetic-Nonferromagnetic Phase Boundary on the Two-Dimensional ±J Ising Model

The ferromagnetic-nonferromagnetic phase boundary on the two-dimensional ± J Ising model in the p - T plane is determined by the use of the coherent-anomaly method (CAM) proposed by Suzuki, where p is the concentration of the + J bond, and T the temperature. The phase boundary below the Nishimori line has been found to be vertical at p =0.884±0.001 to the p -axis, which is consistent with the previous results obtained under the assumption of Suzukis weak universality. The critical exponent γ p ( T ) has also been determined along the phase boundary, which shows a crossover tendency.

Dimer State in Quantum Spin Systems.

The dimer state for the spin-1/2 quantum Heisenberg antiferromagnet is studied using the theory of resonating valence bond. The present theory is systematic and much more simple than the other theories. We obtain two important theorems. By use of them we can get the dimer eigen state in the linear chain, ladder, square and simple cubic lattices by the unified way. If the relations between exchange integrals are satisfied, the obtained dimer eigen state is the ground state.

Determination of the Critical Points of Antiferromagnetic Ising Model with Next Nearest Neighbour Interactions on the Triangular Lattice

Positions of critical temperatures of antiferromagnetic Ising model with ferromagnetic next nearest neighbour interactions on the triangular lattice are investigated by making use of their properties of the Kosterlitz-Thouless type of phase transition. In particular, finite-size scaling method and Monte Carlo Renormalization Group methods (MCRG) with flow diagrams of the anomalous dimension η show the fixed line structure where the correlation length diverges. Another MCRG with flow diagram of the stiffness constant also shows a critical property clearly. The temperature dependence of the long range order is also discussed in order to locate the lower critical point.