Phase transitions in 1-D magnetic materials

Thomas Lorenz

V. L. Pokrovsky

Zhang Zhi-dong, Norman Henry March

Experimental data for critical exponents in some magnetic materials are compared with recent theoretical results on the three-dimensional (3D) Ising model, as derived by one of us (ZDZ) based on two conjectures [Z.D. Zhang, Conjectures on the exact solution of three-dimensional (3D) simple orthorhombic Ising lattices, Phil. Mag. 87 (2007), pp. 5309–5419]. It is found that critical exponents in some bulk magnetic materials indeed form a 3D Ising universality. Our attention is then focused on the critical indices at fluid–fluid phase transition. We suggest to use Zhang's exponent β = 3/8 to fit the experimental data over the wider asymptotic region near the critical point of a fluid–fluid phase transition. The 3D Ising universality should exist for critical indices in a certain class of magnets and at fluid–fluid phase transition.

Omid Nohadani

Rahmat Rahmat, Sri Yunita, Tasrief Surungan

The study of phase transition is an important subject in condensed matter physics as some materials are more versatile when they are at certain phase. The low temperature ferromagnetic phase of magnetic material is a rm example of these. Passing by the Curie temperature, the paramagnetic phase of magnetic materials will change to a ferromagnetic phase. There are three main variables controlling a magnetic phase transition, namely the symmetry of spins, coupling interaction and the lattice structure. It is known that the discreteness can create low temper ature magnetic order, exempli ed by the existence of a true- long range order for the 2D 6-state clock model at lower temperature [1, 2] In this talk we present our study of the ferromagnetic polyhedral spins model on square lattice with bond dilution. Polyhedral spins are the discrete counterpart of the continuous Heisenberg spin model. Two polyhedral spin models, i.e., the icosahedoron and dodecahedron model are discussed. As previously reported, the non-diluted (pure) ferromagnetic case of these models exhibits nite temperature phase transition [3]. We use Monte Carlo simulation with a newly introduced algorithm, two-size PCC algorithm [4]; and probe whether the existing phase transitions are signi cantly a ected by the bond dilution. We simulate the models with various bond concentrations and calculate their corresponding critical temperatures. The phase diagram of the models are presented as a plot of the obtained critical temperatures with respect to their corresponding bond concentrations

Artur Falqueto Sonsin, M R Cortes, D.R.M. Nunes +2 more

We simulate the Ising Model with the Monte Carlo method and use the algorithms of Metropolis to update the distribution of spins. We found that, in the specific case of the three-dimensional Ising Model, methods of Metropolis are efficient. Studying the system near the point of phase transition, we observe that the magnetization goes to zero. In our simulations we analyzed the behavior of the magnetization and magnetic susceptibility to verify the phase transition in a paramagnetic to ferromagnetic material. The behavior of the magnetization and of the magnetic susceptibility as a function of the temperature suggest a phase transition around KT/J ≈ 4.5 and was evidenced the problem of finite size of the lattice to work with large lattice.