Boundary States and Correlation Functions of Tricritical Ising Model from Coulomb-Gas Formalism

We consider the minimal conformaJ model describing the tricritical Ising model on the disk and on the upper half plane. Using the coulomb-gas formalism we determine its consistents boundary states as well as its one-point and two-point correlation functions.     

Tricritical and Critical Exponents in Microcanonical Ensemble of Systems with Long-Range Interactions

We explore the tricritical points and the critical lines of both Blume-Emery-Griffiths and Ising model within long-range interactions in the microcanonical ensemble. For K=K_MTP, the tricritical exponents take the values β=1/4, 1=γ^-≠γ⁺=1/2 and 0=α^-≠α⁺=-1/2, which disagree with classical (mean field) values. When K>K_MTP, the phase transition becomes second order and the critical exponents have classical values except close to the canonical tricritical parameters (K_CTP), where the values of the critical expoents become β=1/2, 1=γ^-≠γ⁺=2 and 0=α⁺≠α⁺=1.     

The thermodynamics of purely elastic scattering theories and conformal perturbation theory

We discuss the thermodynamic Bethe ansatz, and explain how it allows one to reduce the infinite-volume thermodynamics of a (1 + 1)-dimensional purely elastic scattering theory to the solution of a set of integral equations for the one-particle excitation energies. The free energy at zero chemical potential(s) and temperature T is related to the ground state energy E₀(R) of the theory on a cylinder of circumference R = 1/T. E₀(R) determines properties of the CFT describing the UV limit of the given massive theory. These include the central charge (which we investigated in earlier work), the scaling dimension d of the conformal field whose perturbation leads to the massive theory, the coefficients in the conformal perturbation theory (CPT) expansion of E₀(R) in powers of R^2−d, and the bulk term in the CPT calculation of the ground-state energy. We determine the bulk term analytically, and obtain numerically the first six coefficients in the expansion of E₀(R) for many purely elastic scattering theories, including the scaling limit of the T = T_c Ising model in a magnetic field. The perfect agreement with (more limited) direct CPT results provides further strong support for the identification of these theories as specific perturbed CFTs. We suggest that the singularities of E₀(R), the first of which is responsible for the finite radius of convergence of CPT, are square-root branch points and related to the zeros of the partition function of the corresponding lattice model.     

Exact g-function flow between conformal field theories

Exact equations are proposed to describe g-function flows in integrable boundary quantum field theories which interpolate between different conformal field theories in their ultraviolet and infrared limits, extending previous work where purely massive flows were treated. The approach is illustrated with flows between the tricritical and critical Ising models, but the method is not restricted to these cases and should be of use in unravelling general patterns of integrable boundary flows between pairs of conformal field theories.     

The antiferromagnetic Potts model in two dimensions: Berker-Kadanoff phase, antiferromagnetic transition, and the role of Beraha numbers

Using methods of integrable systems and conformal field theory, we study the Q-state Potts model on the square lattice with e^K real. We discover a surprisingly rich phase diagram that involves, besides the usual ferromagnetic critical line, an antiferromagnetic critical line and a Berker-Kadanoff phase (i.e., a massless low-temperature phase with coupling-independent exponents) that has singularities at the Baraha numbers (including Q integer) Q = 4cos²π/n. Critical properties are derived; we show in particular that the Q = 4cos²π/δ antiferromagnetic critical Potts model is in the “Z_δ−2” universality class with c = 2−6/δ. Extensions to other lattices are considered. We discuss the consequences of our results on the coloring problem and the Beraha conjecture. Three appendices deal with the geometrical interpretation of the Temperley-Lieb algebra and U_qsl(2) symmetry in the Potts and associated loops model, and with the vertex-Potts model correspondence in systems with free boundary conditions.     

Steered coherence and entanglement in the Heisenberg XX chain under twisted boundary conditions

We study steered coherence(SC) and entanglement in a three-spin Heisenberg XX model under twisted boundary conditions and show that their strengths can be significantly enhanced by tuning the twist angle. The optimal twist angle θ_(opt) for achieving the maximum l_1 norm of SC is π in the region of weak field B and decreases gradually from π to 0 when B increases after a critical value, while for the relative entropy of SC, θ_(opt) equals π in the weak field region and 0 otherwise.The entanglement and the critical temperature above which the entanglement vanishes can also be significantly enhanced by tuning the twist angle from 0 to π.     

Boundary conditions changing operators in non-conformal theories

Boundary conditions changing operators have played an important role in conformal field theory. Here, we study their equivalent in the case where a mass scale is introduced, in an integrable way, either in the bulk or at the boundary. More precisely, we propose an axiomatic approach to determine the general scalar products _bθ₁, … ,θ_mθ₁′, … ,θ_n′_a, between asymptotic states in the Hilbert spaces with a and b boundary conditions respectively, and compute these scalar products explicitly in the case of the Ising and sinh-Gordon models with a mass and a boundary interaction. These quantities can be used to study statistical systems with inhomogeneous boundary conditions, and, more interestingly maybe, dynamical problems in quantum impurity problems. As an example, we obtain a series of new exact results for the transition probability in the double-well problem of dissipative quantum mechanics.     

Critical currents and the critical state in superconductors with magnetic ions

The critical state model is used to derive equations that relate the additional magnetic moment (ΔM) produced by the flux pinning to the critical current density (J_c) measured in transport measurements. The equations derived for conventional superconductors can be used for superconductors that contain magnetic ions, if ΔM is replaced by ΔM/(1 + χ′(H)) where χ′(H) is the differential susceptibility. In the critical state, the field gradient has contributions from both the macroscopic supercurrents and the Amperian currents from the magnetic ions. Magnetic measurements are sensitive to both contributions. Transport measurements only characterise the macroscopic supercurrents. For superconductors which contain rare-earth elements, the J_c values calculated using hysteretic magnetisation measurements without including the term χ′(H), can be in error by factors of 7.     

Magnetic Properties of Transverse Ising Model under a Time Oscillating Longitudinal Field

A transverse Ising spin system, in the presence of time-dependentlongitudinal field, is studied by the effective-field theory (EFT). Theeffective-field equations of motion of the average magnetization are givenfor the simple cubic lattice (Z = 6) and the honeycomb lattice (Z = 3).The Liapunov exponent λ is calculated for discussing the stability of the magnetization and it is used to determine the phase boundary. Thedynamic phase transition diagrams in h₀/ ZJ -Γ/ZJ plane and in h₀/ZJ-T/ZJ plane have been drawn, and there is no dynamical tricritical point on the dynamic phase transition boundary. The effect of the thermal fluctuations upon the dynamic phase boundary has been discussed.     

Boundary renormalisation group flows of the supersymmetric Lee–Yang model and its extensions

In this paper we examine the supersymmetric Lee–Yang model in the presence of boundaries. We determine the reflection factors for the Neveu–Schwarz type boundary conditions from the reduction of the supersymmetric sine-Gordon model and check them by using boundary truncated conformal space approach in the massless case. We explore the boundary renormalisation groups flows using boundary TBA and TCSA.     

Purely transmitting defect field theories

We define an infinite class of integrable theories with a defect which are formulated as chiral defect perturbations of a conformal field theory. Such theories are massless in the bulk and are purely transmitting through the defect. The integrability of these theories requires the introduction of defect degrees of freedom. Such degrees of freedom lead to a novel set of Yang-Baxter equations. The defect degrees of freedom are identified through folding the chiral defect theories onto massless boundary field theories. The examples of the sine-Gordon theory and Ising model are worked out in some detail.     

Upper critical fields of ferromagnet/superconductor layered structures

The temperature dependence of the upper critical fields, both perpendicular H_c2 and parallel H_c2 to layer planes of ferromagnet/superconductor bi- and multilayers, is theoretically investigated. The secular equation of the superconducting order parameter for determining the phase diagram (H, T) is obtained by solving exactly the linearized Usadel equations in the multimode method taking into account the material parameter values. For the bilayers system, the influence of the boundary resistivity on the critical fields, and the dimensional crossover behavior of H_c2(T) are studied in details. For the multilayered structure, the effects of the π-phase state on both the superconducting transition temperature T_c and the upper critical fields (H_c2, and H_c2) are also considered. The nonmonotonic T_c behaviors are predicted. The interplay between 0- and π-phases leading to the strong oscillations of T_c as well as the temperature dependence of the zero temperature critical fields on the ferromagnetic layer thickness are investigated theoretically.     

Hamiltonian BRST quantization of the conformal string

We present a new formulation of the tensionless string (T = 0) where the space-time conformal symmetry is manifest. Using a Hamiltonian BRST scheme we quantize this Conformal String and find that it has critical dimension D = 2. This is in keeping with our classical result that the model describes massless particles in this dimension. It is also consistent with our previous results which indicate that quantized conformally symmetric tensionless strings describe a topological phase away from D = 2.

We reach our result by demanding nilpotency of the BRST charge and consistency with the Jacobi identities. The derivation is presented in two different ways: in operator language and using mode expansions.

Careful attention is paid to regularization, a crucial ingredient in our calculations.     

Focusing properties of a bounded cylindrical field

Numerical solution of motion equations has been used in the non-relativistic limit in order to determine the focussing properties of the cylindrical field between concentric cylinders of radii R₁, R₂ with two boundaries along the Z-axis, for charged particles entering the field parallel to the symmetry axis. The field is a solution of the Laplace equation ²U(R, Z)=0, with the boundary conditions as follows: U(R₁, Z)=U(R, 0)=U(R, L)=0, U(R₂, Z)=V. It was shown that this field can be used for the energy analysis with second order focussing.     

Spontaneous breaking of scale invariance in a supersymmetric model

The phase structure of a large N, O(N) supersymmetric model in three dimensions is studied. Of special interest is the spontaneous breaking of scale invariance which occurs at a fixed value of the coupling constant, λ₀=λ_c=4π. In this phase the bosons and fermions acquire a mass while a Goldstone boson (dilaton) and Goldstone fermion (“dilatino”) are dynamically generated as massless bound states. The absence of renormalization of the dimensionless coupling constant λ₀ leaves these Goldstone particles massless.     

Globally conformal invariant gauge field theory with rational correlation functions

Operator product expansions (OPE) for the product of a scalar field with its conjugate are presented as infinite sums of bilocal fields V_κ(x₁,x₂) of dimension (κ,κ). For a globally conformal invariant (GCI) theory we write down the OPE of V_κ into a series of twist (dimension minus rank) 2κ symmetric traceless tensor fields with coefficients computed from the (rational) 4-point function of the scalar field.

We argue that the theory of a GCI hermitian scalar field of dimension 4 in D=4 Minkowski space such that the 3-point functions of a pair of 's and a scalar field of dimension 2 or 4 vanish can be interpreted as the theory of local observables of a conformally invariant fixed point in a gauge theory with Lagrangian density .     

Off-criticality behaviour of the Blume-Capel quantum chain as a check of Zamolodchikov's conjecture

Using finite-size numerical calculations, we study the off-criticality behaviour of the Blume-Capel quantum chain in the neighbourhood of the tricritical Ising point. Moving from the tricritical point in the into the disordered region, we find masses and thresholds in agreement with the structure proposed by Zamolodchikov from conformal field theory. Moving in opposite directions, the spectrum is degenerate between the Z₂-even and Z₂-odd sectors, suggesting an underlying supersymmetry. The free-particle energy-momentum relation and the scaling properties off criticality are checked.     

Generalized Einstein manifolds

A Finslerian manifold is called a generalized Einstein manifold (GEM) if the Ricci directional curvature R(u,u) is independent of the direction. Let F⁰(M, g_t) be a deformation of a compact n-dimensional Finslerian manifold preserving the volume of the unitary fibre bundle W(M). We prove that the critical points g₀ F⁰(g_t) of the integral I(g_t) on W(M) of the Finslerian scalar curvature (and certain functions of the scalar curvature) define a GEM. We give an estimate of the eigenvalues of Laplacian Δ defined on W(M) operating on the functions coming from the base when (M, g) is of minima fibration with a constant scalar curvature H admitting a conformal infinitesimal deformation (CID). We obtain λ ≥ H/(n − 1) (Δf = λf). If M is simply connected and λ = H/(n − 1), then (M, g) is Riemannian and is isometric to an n-sphere. We first calculate, in the general case, the formula of the second variationals of the integral I (g_t) for G = g₀, then for a CID we show that for certain Finslerian manifolds, I″(g₀) > 0. Applications to the gravitation and electromagnetism in general relativity are given. We prove that the spaces characterizing Einstein-Maxwell equations are GEMs.