Abstract
The linear perturbation group transformation (LPRG) is used to study the thermodynamics of the axial next-nearest-neighbor Ising model with four spin interactions (extended ANNNI) in a field. The LPRG for weakly interacting Ising chains is presented. The method is used to study finite field para-ferrimagnetic phase transitions observed in layered uranium compounds, UAs_{1-x}Se_x, UPd_2Si_2 or UNi_2Si_2. The above-mentioned systems are made of ferromagnetic layers and the spins from the nearest-neighbor and next-nearest-neighbor layers are coupled by the antiferromagnetic interactions J_1<0 and J_2<0, respectively. Each of these systems exhibits a triple point in which two ordered phases (ferrimagnetic and incommensurate) meet the paramagnetic one, and all undergo the high field phase transition from para- to ferrimagnetic (++-) phase. However, if in UAs_{1-x}Se_x the para-ferri phase transition is of the first order as expected from the symmetry reason, in UT_2Si_2 (T=Pd,Ni) this transition seems to be a continuous one, at least in the vicinity of the multicritical point. Within the MFA, the critical character of the finite field para-ferrimagnetic transition at least at one isolated point can be described by the ANNNI model supplemented by an additional, e.g., four-spin interaction. However, in LPRG approximation for the ratio \kappa=J_2/J_1 around 0.5 there is a critical value of the field for which an isolated critical point also exists in the original ANNNI model. The positive four-spin interaction shifts the critical point towards higher fields and changes the shape of the specific heat curve. In the latter case for the fields small enough, the specific heat exhibits two-peak structure in the paramagnetic phase.
Highlights
The Linear Perturbation Renormalization Group (LPRG) [1] method uses a simple one-dimensional decimation to study universal and non-universal such as a location of the critical temperature and temperature or field dependence of the properties of thermodynamic quantities of several classical and quantum higher-dimensional models
If in UAs1−x Sex the para-ferri phase transition is of the first order, in UT2Si2 this transition, at least in the vicinity of the multicritical point, seems to be a continuous one
Within the MFA it has been shown that the ANNNI model should be supplemented by some additional, e.g., four-spin interaction to exhibit an isolated critical point [17]
Summary
The Linear Perturbation Renormalization Group (LPRG) [1] method uses a simple one-dimensional decimation to study universal (critical) and non-universal such as a location of the critical temperature and temperature or field dependence of the properties of thermodynamic quantities of several classical and quantum higher-dimensional models. The LPRG is used to study the thermodynamics and the existence of a critical point in two-dimensional axial next-nearest-neighbour Ising model with four spin interactions (extended ANNNI) in a field.
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