Critical properties of a three dimensional p-spin model

In this paper we study the critical properties of a finite dimensional generalization of the p-spin model. We find evidence that in dimension three, contrary to its mean field limit, the glass transition is associated to a diverging susceptibility (and correlation length).Comment: 6 Pages, 12 Figure

Antiferromagnetism of Zn2_2VO(PO4)2_4)_2 and the dilution with Ti4+^{4+}

We report static and dynamic properties of the antiferromagnetic compound Zn$_{2}$(VO)(PO$_{4}$)$_{2}$, and the consequences of non-magnetic Ti$^{4+}$ doping at the V$^{4+}$ site. $^{31}$P nuclear magnetic resonance (NMR) spectra and spin-lattice relaxation rate ($1/T_1$) consistently show the formation of the long-range antiferromagnetic order below $T_N= 3.8-3.9$\,K. The critical exponent $\beta=0.33 \pm 0.02$ estimated from the temperature dependence of the sublattice magnetization measured by $^{31}$P NMR at 9.4\,MHz is consistent with universality classes of three-dimensional spin models. The isotropic and axial hyperfine couplings between the $^{31}$P nuclei and V$^{4+}$ spins are $A_{\rm hf}^{\rm iso} = (9221 \pm 100)$ Oe/$\mu_{\rm B}$ and $A_{\rm hf}^{\rm ax} = (1010 \pm 50)$ Oe/$\mu_{\rm B}$, respectively. Magnetic susceptibility data above 6.5\,K and heat capacity data above 4.5\,K are well described by quantum Monte-Carlo simulations for the Heisenberg model on the square lattice with $J\simeq 7.7$\,K. This value of $J$ is consistent with the values obtained from the NMR shift, $1/T_1$ and electron spin resonance (ESR) intensity analysis. Doping Zn$_2$VO(PO$_4)_2$ with non-magnetic Ti$^{4+}$ leads to a marginal increase in the $J$ value and the overall dilution of the spin lattice. In contrast to the recent \textit{ab initio} results, we find neither evidence for the monoclinic structural distortion nor signatures of the magnetic one-dimensionality for doped samples with up to 15\% of Ti$^{4+}$. The N\'eel temperature $T_{\rm N}$ decreases linearly with increasing the amount of the non-magnetic dopant.Comment: 13 pages, 12 figures, 2 table

Entanglement entropy of a three-spin interacting spin chain with a time-reversal breaking impurity at one boundary

We investigate the effect of a time-reversal breaking impurity term on both the equilibrium and non-equilibrium critical properties of entanglement entropy (EE) in a three-spin interacting transverse Ising model which can be mapped to a one-dimensional p-wave superconductor with next-nearest-neighbor hopping. Due to the presence of next-nearest-neighbor hopping, a new topological phase with two zero-energy Majorana modes at each end of an open chain appears in the phase diagram. We show that the derivative of EE with respect to one of the parameters of the Hamiltonian can detect the quantum phase transitions by exhibiting cusp like structure at those points; impurity strength (\la_d) can substantially modify the peak/dip height associated with the cusp. Importantly, we find that the logarithmic scaling of the EE with block size remains unaffected by the application of the impurity term, although, the coefficient (i.e., central charge) varies logarithmically with the impurity strength for a lower range of \la_d and eventually saturates with an exponential damping factor (\sim \exp(-\la_d)) for the phase boundaries shared with the phase containing two Majorana edge modes. On the other hand, it receives a linear correction in term of \la_d for an another phase boundary. Finally, we focus to study the effect of the impurity in the time evolution of the EE for the critical quenching case where impurity term is applied only to the final Hamiltonian. Interestingly, it has been shown that for all the phase boundaries in contrary to the equilibrium case, the saturation value of the EE increases logarithmically with the strength of impurity in a certain region of \la_d and finally, for higher values of \la_d, it increases very slowly which is dictated by an exponential damping factor.Comment: 10 pages, 10 figure

Compensation temperature of 3d mixed ferro-ferrimagnetic ternary alloy

In this study, we have considered the three dimensional mixed ferro-ferrimagnetic ternary alloy model of the type AB$_{p}$C$_{1-p}$ where the A and X (X=B or C) ions are alternately connected and have different Ising spins S$^{A}$=3/2, S$^{B}$=1 and S$^{C}$=5/2, respectively. We have investigated the dependence of the critical and compensation temperatures of the model on concentration and interaction parameters by using MC simulation method. We have shown that the behavior of the critical temperature and the existence of compensation points strongly depend on interaction and concentration parameters. In particular, we have found that the critical temperature of the model is independent on concentration of different types of spins at a special interaction value and the model has one or two compensation temperature points in a certain range of values of the concentration of the different spins.Comment: To be published in JMM

Symmetries of microcanonical entropy surfaces

Symmetry properties of the microcanonical entropy surface as a function of the energy and the order parameter are deduced from the invariance group of the Hamiltonian of the physical system. The consequences of these symmetries for the microcanonical order parameter in the high energy and in the low energy phases are investigated. In particular the breaking of the symmetry of the microcanonical entropy in the low energy regime is considered. The general statements are corroborated by investigations of various examples of classical spin systems.Comment: 15 pages, 5 figures include

Invaded cluster simulations of the XY model in two and three dimensions

The invaded cluster algorithm is used to study the XY model in two and three dimensions up to sizes 2000^2 and 120^3 respectively. A soft spin O(2) model, in the same universality class as the 3D XY model, is also studied. The static critical properties of the model and the dynamical properties of the algorithm are reported. The results are K_c=0.45412(2) for the 3D XY model and eta=0.037(2) for the 3D XY universality class. For the 2D XY model the results are K_c=1.120(1) and eta=0.251(5). The invaded cluster algorithm does not show any critical slowing for the magnetization or critical temperature estimator for the 2D or 3D XY models.Comment: 30 pages, 11 figures, problem viewing figures corrected in v

Phenomenological Renormalization Group Methods

Some renormalization group approaches have been proposed during the last few years which are close in spirit to the Nightingale phenomenological procedure. In essence, by exploiting the finite size scaling hypothesis, the approximate critical behavior of the model on infinite lattice is obtained through the exact computation of some thermal quantities of the model on finite clusters. In this work some of these methods are reviewed, namely the mean field renormalization group, the effective field renormalization group and the finite size scaling renormalization group procedures. Although special emphasis is given to the mean field renormalization group (since it has been, up to now, much more applied an extended to study a wide variety of different systems) a discussion of their potentialities and interrelations to other methods is also addressed.Comment: Review Articl

Random Network Models and Quantum Phase Transitions in Two Dimensions

An overview of the random network model invented by Chalker and Coddington, and its generalizations, is provided. After a short introduction into the physics of the Integer Quantum Hall Effect, which historically has been the motivation for introducing the network model, the percolation model for electrons in spatial dimension 2 in a strong perpendicular magnetic field and a spatially correlated random potential is described. Based on this, the network model is established, using the concepts of percolating probability amplitude and tunneling. Its localization properties and its behavior at the critical point are discussed including a short survey on the statistics of energy levels and wave function amplitudes. Magneto-transport is reviewed with emphasis on some new results on conductance distributions. Generalizations are performed by establishing equivalent Hamiltonians. In particular, the significance of mappings to the Dirac model and the two dimensional Ising model are discussed. A description of renormalization group treatments is given. The classification of two dimensional random systems according to their symmetries is outlined. This provides access to the complete set of quantum phase transitions like the thermal Hall transition and the spin quantum Hall transition in two dimension. The supersymmetric effective field theory for the critical properties of network models is formulated. The network model is extended to higher dimensions including remarks on the chiral metal phase at the surface of a multi-layer quantum Hall system.Comment: 176 pages, final version, references correcte