Renormalization of the critical exponents in the “be” compressible Ising model

K. A. Penson

The critical behavior of a compressible Ising system of the Baker-Essam type is examined for positive pressures. In addition to satisfying the assumptions of Fisher's theory of renormalization of critical exponents, the model, allows one to calculate the temperature region around ${T}_{c}$ where the renormalized exponents should show up. The region is $\ensuremath{\Delta}{T}_{\ifmmode\times\else\texttimes\fi{}}\ensuremath{\sim}{(P{J}_{1}^{2})}^{\frac{1}{\ensuremath{\alpha}}}$ for small pressures, where ${J}_{1}$ is the spin-lattice coupling and $\ensuremath{\alpha}$ is the specific-heat exponent of the corresponding rigid Ising system.

J. A. Plascak, W. Figueiredo

Yonathan Shapir, Serge Galam

The interplay between disorder and compressibility in Ising magnets is studied. Contrary to pure systems in which a weak compressibility drives the transition first order, we find from a renormalization group analysis that it has no effect on disordered systems which keep undergoing continuous transition with rigid random-bond Ising model critical exponents. The mean field calculation exhibits a dilution-dependent tricritical point beyond which, at stronger compressibility the transition is first order. The different behavior of XY and Heisenberg magnets is discussed.

Aleksandr Pishtshev

Zhibing Li, Zhigang Shuai, Q Wang +2 more

The symmetric two-layer Ising model (TLIM) is studied by the corner transfer matrix renormalization group method. The critical points and critical exponents are calculated. It is found that the TLIM belongs to the same universality class as the Ising model. The shift exponent is calculated to be 1.773, which is consistent with the theoretical prediction of 1.75 with 1.3% deviation.

Bikas K. Chakrabarti