Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userPhase Transition of the Ising Model on Fractal Lattice
118
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
The competition between interactions and dissipative processes in a quantum many-body system can drive phase transitions of different order. Exploiting a combination of cluster methods and quantum trajectories, we show how the systematic inclusion of (classical and quantum) nonlocal correlations at increasing distances is crucial to determine the structure of the phase diagram, as well as the nature of the transitions in strongly interacting spin systems. In practice, we focus on the paradigmatic dissipative quantum Ising model: in contrast to the non-dissipative case, its phase diagram is still a matter of debate in the literature. When dissipation acts along the interaction direction, we predict important quantitative modifications of the position of the first-order transition boundary. In the case of incoherent relaxation in the field direction, our approach confirms the presence of a second-order transition, while does not support the possible existence of multicritical points. Potentially, these results can be tested in up-to date quantum simulators of Rydberg atoms.
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.
We investigate the role of a transverse field on the Ising square antiferromagnet with first-($J_1$) and second-($J_2$) neighbor interactions. Using a cluster mean-field approach, we provide a telltale characterization of the frustration effects on the phase boundaries and entropy accumulation process emerging from the interplay between quantum and thermal fluctuations. We found that the paramagnetic (PM) and antiferromagnetic phases are separated by continuous phase transitions. On the other hand, continuous and discontinuous phase transitions, as well as tricriticality, are observed in the phase boundaries between PM and superantiferromagnetic phases. A rich scenario arises when a discontinuous phase transition occurs in the classical limit while quantum fluctuations recover criticality. We also find that the entropy accumulation process predicted to occur at temperatures close to the quantum critical point can be enhanced by frustration. Our results provide a description for the phase boundaries and entropy behavior that can help to identify the ratio $J_2/J_1$ in possible experimental realizations of the quantum $J_1$-$J_2$ Ising antiferromagnet.
The transverse-field Ising model on the Sierpinski fractal, which is characterized by the fractal dimension $log_2^{~} 3 approx 1.585$, is studied by a tensor-network method, the Higher-Order Tensor Renormalization Group. We analyze the ground-state energy and the spontaneous magnetization in the thermodynamic limit. The system exhibits the second-order phase transition at the critical transverse field $h_{rm c}^{~} = 1.865$. The critical exponents $beta approx 0.198$ and $delta approx 8.7$ are obtained. Complementary to the tensor-network method, we make use of the real-space renormalization group and improved mean-field approximations for comparison.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
