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Register a new userExact solution of the one-dimensional spin-$frac32$ Ising model in magnetic field
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In this paper, we study the Ising model with general spin $S$ in presence of an external magnetic field by means of the equations of motion method and of the Greens function formalism. First, the model is shown to be isomorphic to a fermionic one constituted of $2S$ species of localized particles interacting via an intersite Coulomb interaction. Then, an exact solution is found, for any dimension, in terms of a finite, complete set of eigenoperators of the latter Hamiltonian and of the corresponding eigenenergies. This explicit knowledge makes possible writing exact expressions for the corresponding Greens function and correlation functions, which turn out to depend on a finite set of parameters to be self-consistently determined. Finally, we present an original procedure, based on algebraic constraints, to exactly fix these latter parameters in the case of dimension 1 and spin $frac32$. For this latter case and, just for comparison, for the cases of dimension 1 and spin $frac12$ [F. Mancini, Eur. Phys. J. B textbf{45}, 497 (2005)] and spin 1 [F. Mancini, Eur. Phys. J. B textbf{47}, 527 (2005)], relevant properties such as magnetization $<S>$ and square magnetic moment $<S^2 >$, susceptibility and specific heat are reported as functions of temperature and external magnetic field both for ferromagnetic and antiferromagnetic couplings. It is worth noticing the use we made of composite operators describing occupation transitions among the 3 species of localized particles and the related study of single, double and triple occupancy per site.
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High-field specific heat measurements on BaCo2V2O8, which is a good realization of an S = 1/2 quasi one-dimensional Ising-like antifferomagnet, have been performed in magnetic fields up to 12 T along the chain and at temperature down to 200 mK. We have found a new magnetic ordered state in the field-induced phase above Hc ~ 3.9 T. We suggest that a novel type of the incommensurate order, which has no correspondence to the classical spin system, is realized in the field-induced phase.
The quantum Kibble-Zurek mechanism (QKZM) predicts universal dynamical behavior in the vicinity of quantum phase transitions (QPTs). It is now well understood for one-dimensional quantum matter. Higher-dimensional systems, however, remain a challenge, complicated by fundamental differences of the associated QPTs and their underlying conformal field theories. In this work, we take the first steps towards exploring the QKZM in two dimensions. We study the dynamical crossing of the QPT in the paradigmatic Ising model by a joint effort of modern state-of-the-art numerical methods. As a central result, we quantify universal QKZM behavior close to the QPT. However, upon traversing further into the ferromagnetic regime, we observe deviations from the QKZM prediction. We explain the observed behavior by proposing an {it extended QKZM} taking into account spectral information as well as phase ordering. Our work provides a starting point towards the exploration of dynamical universality in higher-dimensional quantum matter.
In this paper we present for the first time the exact solution in the narrow-band limit of the 1D extended Hubbard model with nearest-neighbour spin-spin interactions described by an exchange constant J. An external magnetic field h is also taken into account. This result has been obtained in the framework of the Greens functions formalism, using the Composite Operator Method. By means of this theoretical background, we have studied some relevant features such as double occupancy, magnetization, spin-spin and charge-charge correlation functions and derived a phase diagram for both ferro (J>0) and anti-ferro (J<0) coupling in the limit of zero temperature. We also report a study on density of states, specific heat, charge and spin susceptibilities. In the limit of zero temperature, we show that the model exhibits a very rich phase diagram characterized by different magnetic orders and by the coexistence of charge and spin orderings at commensurate filling. Moreover, our analysis at finite temperature of density of states and response functions shows the presence of low-temperature charge and spin excitations near the phase boundaries.
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