A quantum spin model with three-spin coupling is studied by finite-lattice methods. The critical indices nu and alpha are obtained by standard finite-size scaling analysis. Conformal invariance is used to estimate the exponents nu and eta , the central charge or conformal anomaly c and the anomalous dimension of a spin 1/4 parafermion. The authors conclude that the model belongs to the same universality class as the four-state Potts and Baxter-Wu models, although the convergence of the various finite lattice estimators is extremely slow.
The ground-state properties of a quantum spin chain with three-spin couplings are investigated using finite-size calculations. The results are compared with the predictions of conformal invariance for finite systems at the critical point. The critical point. The critical exponents eta E and eta S of energy density and spin correlation functions are calculated and estimated to be eta E approximately=1.30 and eta S approximately=0.25. The results suggest that this model is conformally invariant with a central charge very close to or equal to one.
The
q-state Potts chain with ferromagnetic couplings,
J=1, in the presence of a transverse field $\mathrm{\ensuremath{\Gamma}}$ has a quantum phase transition at $\mathrm{\ensuremath{\Gamma}}/q=1$, which is continuous for $q\ensuremath{\le}4$ and of first order for
q>4. Here we introduce a
q-periodic alternating longitudinal field of strength
h and study the phase diagram and the critical properties of the model. For $h<q/(q\ensuremath{-}1)$, there is a ferromagnetic ordered phase, for $\mathrm{\ensuremath{\Gamma}}<{\mathrm{\ensuremath{\Gamma}}}_{c}(h)$, and at $h=q/(q\ensuremath{-}1)$, there is a classical endpoint at $\mathrm{\ensuremath{\Gamma}}=0$, with finite entropy at
T=0. We considered the
q=3 model and using density matrix renormalization group techniques, we calculated the low-lying spectrum of the Hamiltonian, the transverse magnetization, and the spin-spin correlation function, all of which signal a diverging correlation length at the transition point with the exponent of the three-state Potts model. In the vicinity of the classical endpoint, the model is mapped to a quantum hard rod model, which also belongs to the universality class of the ferromagnetic three-state Potts model. Also, the spectrum of the critical Hamiltonian is found in agreement with conformal invariance. At the same time, the correlation function shows a jump at the transition point, and thus the transition is of mixed order for $h<q/(q\ensuremath{-}1)$.
The phase diagram and the critical behavior of the spin-1 and the spin-3/2 two-dimensional Baxter-Wu model in a crystal field are studied by conventional finite-size scaling and conformal invariance theory. The phase diagram of this model, for the spin-1 case, is qualitatively the same as those of the diluted 4-states Potts model and the spin-1 Blume-Capel model. However, for the present case, instead of a tricritical point one has a pentacritical point for a finite value of the crystal field, in disagreement with previous work based on finite-size calculations. On the other hand, for the spin-3/2 case, the phase diagram is much richer and can present, besides a pentacritical point, an additional multicritical end point. Our results also support that the universality class of the critical behavior of the spin-1 and spin-3/2 Baxter-Wu model in a crystal field is the same as the pure Baxter-Wu model, even at the multicritical points.
Finite-Size-Scaling and Conformal Invariance are used in order to find the phase diagram and critical exponents of a quantum spin chain with spin
S=3/2. The model has a tetracritical point besides critical lines. The conformal anomaly and anomalous dimensions of some primary operators are calculated at the tetracritical point.