The effect of dilution on spin systems with competing long- and short-range interactions is studied via explicit calculations on an exactly solvable one-dimensional Ising Hamilton. New dilution-induced phase transitions appear, and a complex phase structure is revealed.
The research of one-dimensional Ising model with the different number of neighbors and the different sign of the exchange integral were performed. The clustered order parameter is proposed for the description of the magnetic transition in spin systems regardless of the sign of the exchange integral and the number of neighbors. The method of calculation of critical field to change the magnetic states was presented. For diluted 1D antiferromagnetic model two plateaus in magnetization behavior are observed, and explained. Influence of length of interaction plays critical role for phase transition of dipoles system. Dipoles on hexagonal lattice show the phase transition only in model of long range interaction, and there isn't critical behavior for short range. The approach to calculation of spin system in Heisenberg model is proposed.
A central quantity of importance for ultracold atoms is contact, which measures two-body correlations at short distances in dilute systems. It appears in universal relations among thermodynamic quantities, such as large momentum tails, energy and dynamic structure factors, through the renowned Tan relations. However, a conceptual question remains open as to whether or not contact can signify phase transitions that are insensitive to short-range physics. Here we show that, near a continuous classical or quantum phase transition, contact exhibits a variety of critical behaviours, including scaling laws and critical exponents that are uniquely determined by the universality class of the phase transition, and a constant contact per particle. We also use a prototypical exactly solvable model to demonstrate these critical behaviours in one-dimensional strongly interacting fermions. Our work establishes an intrinsic connection between the universality of dilute many-body systems and universal critical phenomena near a phase transition.
The linear-perturbation real space renormalization transformation (LPRG) is presented and applied to the study of quantum spin chains coupled by interchain interaction (k 1 ) weaker than intrachain one (k).The method is examined in two exact solvable cases: Ising chains on the square and triangular lattices and quantum XY chain.For the Ising model, in the second order in the cumulant epansion, the deviation of the critical temperature from the exact value is less than 1% for 0.5k > k 1 > 0.15k, but even in the case of the standard Ising model (k 1 = k) we found the value of Tc which differs by 2% from the exact one.For the quantum XY chain the deviation of the free energy value found by using LPRG from the exact Katsura result is less than 1% for T /J > 1, and for rather low temperature T /J = 0.08 is about 6%.The LPRG is used to study the effects of interchain frustration on the phase transition in 2D Heisenberg spin chains with easy axis along the z direction.It is shown that contrary to the pure Ising model in systems with in-plane interactions (XY), the interchain frustration does not destroy the finite-temperature transition.However, such a frustration changes the character of the phase transition from Ising-like to, probably, Kosterlitz-Thouless-like.We have also applied the LPRG method to the calculation of the isothermal magnetocaloric coefficient (M T ) for several spin models in disordered phases.Is is demonstrated that in the presence of antiferromagnetic fluctuations, M T changes sign at some value of the magnetic field.Generally, M T is negative if magnetic field competes with a short-range order, and consequently it can be an indicator of the change in the short-range correlation.