Phase-Transitions in Systems with Competing Short - and Long-Range Interactions.

Lorenz Hruby, Renate Landig, Nishant Dogra +4 more

Yaroslav Ispolatov

István Daruka, Zsolt Gulácsi

We present exact four-spin- and string-correlation functions derived for an Ising chain with competing geometrical nearest-neighbor short-range and mirror-image-type long-range interactions. Unusual $T\ensuremath{\ne}0$ correlation effects were found, indicating qualitative changes in the behavior of the system in different T domains. These domains are not separated by a sharp, traditional phase transition, but are delimited by a temperature ${T}_{i}$ at which the exact connected four-spin-correlation function vanishes. At the same ${T}_{i}$ the pair-correlation function changes its character: The functional form of the correlation length and the nature of the long-range decay are modified.

T. Riste, Sherrington, David

С. В. Белим

In this article, spin systems with competing interactions in an external magnetic field are investigated. The Ising model with ferromagnetic short-range forces and long-range antiferromagnetic forces is considered. Long-range forces decrease according to the power law. Long-range interaction is characterized by the rate of decrease with distance and relative intensity. The Metropolis algorithm is used for computer modeling. Two order parameters for ferromagnetic and antiferromagnetic ordering are used. The theory of finite size scaling is used. The transition temperature was defined based on Binder's cumulants for each of the order parameters. The phase diagram for the system is constructed at various values of the long-range interaction parameters. As the temperature decreases, the system can transfer from the paramagnetic phase into the ferromagnetic and antiferromagnetic ones. The type of the low-temperature phase depends on the intensity of long-range forces and does not depend on the rate of decrease of the interaction with distance. There is a boundary value of the intensity of long-range forces, below which the ferromagnetic phase is implemented, and above it is the antiferromagnetic phase. The change in the phase diagram under the influence of an external magnetic field is investigated. In an external magnetic field, the ferromagnetic phase transition becomes spread. The temperature of the antiferromagnetic phase transition in an external field decreases according to the square law. The boundary value of the intensity of long-range forces linearly grows with increasing the intensity of the external magnetic field. An increase in the boundary value in a magnetic field leads to a change in the type of the low-temperature phase. This effect is shown as a phase transition from the antiferromagnetic to the ferromagnetic phase in the external magnetic field. A comparison with the data of real experiments is carried out.

S. Ramasesha

A Monte Carlo simulation of Ising chains with competing short-range and infinite-range interactions has been carried out. Results show that whenever the system does not enter a metastable state, variation of temperature brings about phase transitions in the Ising chain. These phase transitions, except for two sets of interaction strengths are generally of higher order and involve changes in the long-range while the short-range order remains unaffected.