Sharif Digital Repository

A numerical method based on the transfer matrix method is developed to calculate the critical temperature of two-layer Ising ferromagnet with a weak inter-layer coupling. The reduced internal energy per site has been accurately calculated for symmetric ferromagnetic case, with the nearest neighbor coupling K1 = K2 = K (where K1 and K2 are the nearest neighbor interaction in the first and second layers, respectively) with inter-layer coupling J. The critical temperature as a function of the inter-layer coupling ξ = J/K, is obtained for very weak inter-layer interactions, ξ < 0.1. Also a different function is given for the case of the strong inter-layer interactions (ξ > 1). The importance of... 

Recent developments in the field of applied nanoscience and nanotechnology have heightened the need for categorizing various characteristics of nanostructures. In this regard, this paper establishes a novel method to investigate magnetic properties (phase diagram and spontaneous magnetization) of a cylindrical Ising nanotube. Using a two-layer Ising model and the core-shell concept, the interactions within nanotube has been modelled. In the model, both ferromagnetic and antiferromagnetic cases have been considered. Furthermore, the effect of nanotube's length on the critical temperature is investigated. The model has been simulated using cellular automata approach and phase diagrams were... 

We show that the two-dimensional (12D) Ising model is complete, in the sense that the partition function of any lattice model on any graph is equal to the partition function of the 2D Ising model with complex coupling. The latter model has all its spin-spin coupling equal to iπ4 and all parameters of the original model are contained in the local magnetic fields of the Ising model. This result has already been derived by using techniques from quantum information theory and by exploiting the universality of cluster states. Here we do not use the quantum formalism and hence make the completeness result accessible to a wide audience. Furthermore, our method has the advantage of being algorithmic... 

Recent empirical results have demonstrated that generalized belief propagation (GBP) can be used to closely estimate the capacity of certain 2D runlength-limited constraints. We provide a partial analytical validation of these observations by showing that GBP yields a lower bound on the partition function of 2D Ising models with restricted grid size. While previous papers have proved that belief propagation (BP) can be used to obtain a lower bound on the partition function of 2D Ising models, this paper is the first work that analyzes GBP-based partition function approximations of 2D Ising models  

We have studied the isoheight lines on the WO3 surface as a physical candidate for conformally invariant curves. We have shown that these lines are conformally invariant with the same statistics of domain walls in the critical Ising model. They belong to the family of conformal invariant curves called Schramm-Loewner evolution (or SLEκ), with diffusivity of κ∼3. This can be regarded as the first experimental observation of SLE curves. We have also argued that Ballistic Deposition (BD) can serve as a growth model giving rise to contours with similar statistics at large scales. © 2008 The American Physical Society  

We review a recent development in theoretical understanding of the quenched averaged correlation functions of disordered systems and the logarithmic conformal field theory (LCFT) in d-dimensions. The logarithmic conformal field theory is the generalization of the conformal field theory when the dilatation operator is not diagonal and has the Jordan form. It is discussed that at the random fixed point the disordered systems such as random-bond Ising model, Polymer chain, etc. are described by LCFT and their correlation functions have logarithmic singularities. As an example we discuss in detail the application of LCFT to the problem of random-bond Ising model in 2 ≤ d ≤ 4  

A method is developed to calculate the critical line of two dimensional (2D) anisotropic Ising model including nearest-neighbor interactions. The method is based on the real-space renormalization group (RG) theory with increasing block sizes. The reduced temperatures, Ks (where K=J/kBT and J, kB, and T are the spin coupling interaction, the Boltzmann constant, and the absolute temperature, respectively), are calculated for different block sizes. By increasing the block size, the critical line for three types of lattice, namely: triangular, square, and honeycomb, is obtained and found to compare well with corresponding results reported by Onsager in the thermodynamic limit. Our results also... 

We study the Kitaev-Ising model, where ferromagnetic Ising interactions are added to the Kitaev model on a lattice. This model has two phases which are characterized by topological and ferromagnetic order. Transitions between these two kinds of order are then studied on a quasi-one-dimensional system, on a ladder, and on a two-dimensional periodic lattice, a torus. By exactly mapping the quasi-one-dimensional case to an anisotropic XY chain we show that the transition occurs at zero λ, where λ is the strength of the ferromagnetic coupling. In the two-dimensional case the model is mapped to a two-dimensional Ising model in transverse field, where it shows a transition at a finite value of λ.... 

Ground-state fidelity (GSF) and quantum renormalization group (QRG) theory have proven to be useful tools in the study of quantum critical systems. Here we lay out a general, unified formalism of GSF and QRG; specifically, we propose a method for calculating GSF through QRG, obviating the need for calculating or approximating ground states. This method thus enhances the characterization of quantum criticality as well as scaling analysis of relevant properties with system size. We illustrate the formalism in the one-dimensional Ising model in a transverse field (ITF) and the anisotropic spin-1/2 Heisenberg (XXZ) model. Explicitly, we find the scaling behavior of the GSF for the ITF model in... 

We study the effect of quantum fluctuations by means of a transverse magnetic field (Γ) on the antiferromagnetic J1-J2 Ising model on the checkerboard lattice, the two dimensional version of the pyrochlore lattice. The zero-temperature phase diagram of the model has been obtained by employing a plaquette operator approach (POA). The plaquette operator formalism bosonizes the model, in which a single boson is associated to each eigenstate of a plaquette and the inter-plaquette interactions define an effective Hamiltonian. The excitations of a plaquette would represent an-harmonic fluctuations of the model, which lead not only to lower the excitation energy compared with a single-spin flip but... 

We study the zero-Temperature phase diagram of transverse field Ising model on the J 1-J 2 square lattice. In zero magnetic field, the model has a classical Néel phase for J 2/J 1 < 0.5 and an antiferromagnetic collinear phase for J 2/J 1 > 0.5. We incorporate harmonic fluctuations by using linear spin wave theory (LSWT) with single spin flip excitations above a magnetic order background and obtain the phase diagram of the model in this approximation. We find that harmonic quantum fluctuations of LSWT fail to lift the large degeneracy at J 2/J 1 = 0.5 and exhibit some inconsistent regions on the phase diagram. However, we show that anharmonic fluctuations of cluster operator approach (COA)... 

We formulate a quantum formalism for the statistical mechanical models of discretized field theories on lattices and then show that the discrete version of φ4 theory on 2D square lattice is complete in the sense that the partition function of any other discretized scalar field theory on an arbitrary lattice with arbitrary interactions can be realized as a special case of the partition function of this model. To achieve this, we extend the recently proposed quantum formalism for the Ising model and its completeness property to the continuous variable case  

We investigate a one-dimensional (1-D) Ising model for finite-site systems. The finite-site free energy and the surface free energy are calculated via the transfer matrix method. We show that, at high magnetic fields, the surface free energy has an asymptotic limit. The absolute surface energy increases when the value of f (the ratio of magnetic field to nearest-neighbor interactions) increases, and for f ≥10 approaches a constant value. For the values of f ≥0.2, the finite-site free energy also increases, but slowly. The thermodynamic limit in which physical properties approach the bulk value is also explored  

Ising models in nanosystems are studied in the presence of a magnetic field. For a one-dimensional (1-D) array of spins interacting via nearest-neighbour and next-nearest-neighbour interactions we calculate the heat capacity, the surface energy, the finite-size free energy and the bulk free energy per site. The heat capacity versus temperature exhibits a common wide peak for systems of any size. A small peak also appears at lower temperatures for small arrays when the ratio of magnetic field spin interaction energy over the nearest-neighbour spin-spin interaction energy, f, is within 0 < F ≤ 0.10 . The peak becomes smaller for longer array and eventually vanishes for long arrays,...