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Register a new userPhase transition of the four-dimensional cross-polytope model
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Thermodynamic properties of the four-dimensional cross-polytope model, the 16-cell model, which is an example of higher dimensional generalizations of the octahedron model, are studied on the square lattice. By means of the corner transfer matrix renormalization group (CTMRG) method, presence of the first-order phase transition is confirmed. The latent heat is estimated to be $L_4^{~} = 0.3172$, which is larger than that of the octahedron model $L_3^{~} = 0.0516$. The result suggests that the latent heat increases with the internal dimension $n$ when the higher-dimensional series of the cross-polytope models is considered.
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In this work we have used extensive Monte Carlo simulations and finite size scaling theory to study the phase transition in the dipolar Planar Rotator model (dPRM), also known as dipolar XY model. The true long-range character of the dipolar interactions were taken into account by using the Ewald summation technique. Our results for the critical exponents does not fit those from known universality classes. We observed that the specific heat is apparently non-divergent and the critical exponents are $ u=1.277(2)$, $beta=0.2065(4)$ and $gamma=2.218(5)$. The critical temperature was found to be $T_c=1.201(1)$. Our results are clearly distinct from those of a recent Renormalization Group study from Maier and Schwabl [PRB 70, 134430 (2004)] and agrees with the results from a previous study of the anisotropic Heisenberg model with dipolar interactions in a bilayer system using a cut-off in the dipolar interactions [PRB 79, 054404 (2009)].
We introduce and analyze an exactly soluble one-dimensional Ising model with long range interactions which exhibits a mixed order transition (MOT), namely a phase transition in which the order parameter is discontinuous as in first order transitions while the correlation length diverges as in second order transitions. Such transitions are known to appear in a diverse classes of models which are seemingly unrelated. The model we present serves as a link between two classes of models which exhibit MOT in one dimension, namely, spin models with a coupling constant which decays as the inverse distance squared and models of depinning transitions, thus making a step towards a unifying framework.
Phase transition of the Ising model is investigated on a planar lattice that has a fractal structure. On the lattice, the number of bonds that cross the border of a finite area is doubled when the linear size of the area is extended by a factor of four. The free energy and the spontaneous magnetization of the system are obtained by means of the higher-order tensor renormalization group method. The system exhibits the order-disorder phase transition, where the critical indices are different from that of the square-lattice Ising model. An exponential decay is observed in the density matrix spectrum even at the critical point. It is possible to interpret that the system is less entangled because of the fractal geometry.
The two-dimensional (zero magnetic field) Ising model is known to undergo a second order para-ferromagnetic phase transition, which is accompanied by a correlated percolation transition for the Fortuin-Kasteleyn (FK) clusters. In this paper we uncover that there exists also a second temperature $T_{text{eb}}<T_c$ at which the elastic backbone of FK clusters undergoes a second order phase transition to a dense phase. The corresponding universality class, which is characterized by determining various percolation exponents, is shown to be completely different from directed percolation, proposing a new anisotropic universality class with $beta=0.54pm 0.02$, $ u_{||}=1.86pm 0.01$, $ u_{perp}=1.21pm 0.04$ and $d_f=1.53pm 0.03$. All tested hyper-scaling relations are shown to be valid.
We study the phase transition of the Ising model in networks with core-periphery structures. By Monte Carlo simulations, we show that prior to the order-disorder phase transition the system organizes into an inhomogeneous intermediate phase in which core nodes are much more ordered than peripheral nodes. Interestingly, the susceptibility shows double peaks at two distinct temperatures. We find that, if the connections between core and periphery increase linearly with network size, the first peak does not exhibit any size-dependent effect, and the second one diverges in the limit of infinite network size. Otherwise, if the connections between core and periphery scale sub-linearly with the network size, both peaks of the susceptibility diverge as power laws in the thermodynamic limit. This suggests the appearance of a double transition phenomenon in the Ising model for the latter case. Moreover, we develop a mean-field theory that agrees well with the simulations.
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