It is difficult to derive the solid-fluid transition from microscopic models. We introduce particle systems whose potentials do not decay with distance and calculate their partition function exactly using a method similar to that for lattice systems with infinite-range interaction. In particular, we investigate the behaviors of examples among these models, which become a triangular, body-centered cubic, face-centered cubic, or simple cubic lattice in low-temperature phase. The transitions of the first three examples are of the first order, and that of the last example is of the second order. Note that we define the solid phase as that whose order parameter, or Fourier component of the density, becomes nonzero, and the models we considered obey the ideal-gas law even in the solid phase.
We study field-induced phase transitions in the two-dimensional dipolar Ising ferromagnet with a specific ratio between the exchange and dipolar constants, δ = 1, which exhibits a stripe-ordered phase with the width of one lattice unit at low temperatures without magnetic field. By using a mean-field (MF) approximation and a Monte Caro (MC) method with the stochastic-cutoff algorithm, which is an O(N ) simulation method, we show the temperature-field phase diagrams. In the MC study the orientational order and the structure factor are evaluated. Second-order transition points are determined by a finite-size-scaling analysis and first-order transition points are identified by the analysis of the energy histogram. Although both the MF and MC phase diagrams consist of wide regions of several stripe-ordered phases and narrow regions between them characterized by complicated stripe patterns, they show qualitative and quantitative differences in possible phases and phase boundaries. In the MF phase diagram, three main stripe-ordered phases exhibit a nesting structure, while in the MC phase diagram, two main stripe-ordered phases are located separately, which causes a characteristic field-induced reentrant transition of the orientational order. *
We propose a model of magnetic friction and investigate the relation between the frictional force and the relative velocity of surfaces in the steady state. The model comprises two square lattices adjacent to each other, the upper of which is subjected to an external force, and the magnetic interaction acts as a kind of "potential barrier" that prevents the upper lattice from moving. We consider two surface types for the upper lattice: smooth and rough. The behavior of this model is classified into three domains, which we refer to as domains I,II, and III. In domain I, the external force is weak and cannot move the lattice, whereas in domain III, the external force is dominant compared with other forces. In the intermediate domain II, the frictional force obeys the Dieterich-Ruina law. This characteristic property can be observed regardless of whether the surface is smooth or rough.
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