Quantum criticality in dimerised anisotropic spin-1 chains

Applying the (infinite) density-matrix renormalisation group technique, we explore the effect of an explicit dimerisation on the ground-state phase diagram of the spin-1 XXZ chain with single-ion anisotropy D. We demonstrate that the Haldane phase between large-D and antiferromagnetic phases survives up to a critical dimerisation only. As a further new characteristic the dimerisation induces a direct continuous Ising quantum phase transition between the large-D and antiferromagnetic phases with central charge $$c=1/2$$ c = 1 / 2 , which terminates at a critical end-point where $$c=7/10$$ c = 7 / 10 . Calculating the critical exponents of the order parameter, neutral gap and spin–spin-correlation function, we find $$\beta =1/8$$ β = 1 / 8 (1/24), $$\nu =1$$ ν = 1 (5/9), and $$\eta =1/4$$ η = 1 / 4 (3/20), respectively, which proves the Ising (tricritical Ising) universality class in accordance with field-theoretical predictions.

Вариационная модель низкоразмерного магнетика

A variational method with nonlocal trial function is developed for quantum one-dimensional systems. It is applied to the XXZ spin-1/2 chain with an alternating magnetic field. A four-node trial wave function for the fermionic representation of the model is constructed. The results obtained in the model with an extended trial wave function demonstrate a significant increase in the accuracy of the ground state energy in the region of critical behavior compared with the solutions obtained previously. A method for calculation of the spin correlation function are discussed.

Grassmannization of the 3D Ising Model

The application of Feynman’s diagrammatic technique to classical link models with local constraints seems impossible due to (i) the absence of a free Gaussian theory on top of which the perturbative expansion can be constructed, and (ii) Dyson’s collapse argument, rendering the perturbative expansion divergent. However, we show for the classical 3D Ising model how both problems can be circumvented using a Grassmann representation. This makes it possible to obtain an expansion of the spin correlation function and the magnetic susceptibility in terms of the inverse temperature in the thermodynamic limit, through which the values for the critical temperature and critical index g are evaluated within 1.6% and 5.4% of their accepted values, respectively. Our work is a straightforward adaptation of the theory previously developed in an earlier paper.

Critical phenomena in 1D Ising model with arbitrary spin

The aim of this work was to study critical phenomena taking place in 1D Ising model with different exchange interactions signs and arbitrary spin values in a magnetic field. Exact analytical formulas for frustration fields, zero temperature magnetization and entropy at these fields are obtained. The general behavior of pair spin correlation function with the accounting of only interactions between nearest neighbors is examined.