46 research outputs found
New quantum phase transitions in the two-dimensional J1-J2 model
We analyze the phase diagram of the frustrated Heisenberg antiferromagnet,
the J1-J2 model, in two dimensions. Two quantum phase transitions in the model
are already known: the second order transition from the Neel state to the spin
liquid state at (J_2/J_1)_{c2}=0.38, and the first order transition from the
spin liquid state to the collinear state at (J_2/J_1)_{c4}=0.60. We have found
evidence for two new second order phase transitions: the transition from the
spin columnar dimerized state to the state with plaquette type modulation at
(J_2/J_1)_{c3}=0.50(2), and the transition from the simple Neel state to the
Neel state with spin columnar dimerization at (J_2/J_1)_{c1}=0.34(4). We also
present an independent calculation of (J_2/J_1)_{c2}=0.38 using a new approach.Comment: 3 pages, 5 figures; added referenc
Perturbation theories for the S=1/2 spin ladder with four-spin ring exchange
The isotropic S=1/2 antiferromagnetic spin ladder with additional four-spin
ring exchange is studied perturbatively in the strong coupling regime with the
help of cluster expansion technique, and by means of bosonization in the weak
coupling limit. It is found that a sufficiently large strength of ring exchange
leads to a second-order phase transition, and the shape of the boundary in the
vicinity of the known exact transition point is obtained. The critical exponent
for the gap is found to be , in agreement both with exact results
available for the dimer line and with the bosonization analysis. The phase
emerging for high values of the ring exchange is argued to be gapped and
spontaneously dimerized. The results for the transition line from strong
coupling and from weak coupling match with each other naturally.Comment: 8 pages, 4 figures, some minor changes in text and reference
Statistical Mechanics of the Self-Gravitating Gas: I. Thermodynamic Limit and Phase Diagram
We provide a complete picture to the selfgravitating non-relativistic gas at
thermal equilibrium using Monte Carlo simulations, analytic mean field methods
(MF) and low density expansions. The system is shown to possess an infinite
volume limit in the grand canonical (GCE), canonical (CE) and microcanonical
(MCE) ensembles when(N, V) --> infinity, keeping N/ V^{1/3} fixed. We compute
the equation of state (we do not assume it as is customary), as well as the
energy, free energy, entropy, chemical potential, specific heats, compressibi-
lities and speed of sound;we analyze their properties, signs and singularities.
All physical quantities turn out to depend on a single variable eta = G m^2 N/
[V^{1/3} T] that is kept fixed in the N--> infinity and V --> infinity limit.
The system is in a gaseous phase for eta < eta_T and collapses into a dense
objet for eta > \eta_T in the CE with the pressure becoming large and negative.
At eta simeq eta_T the isothermal compressibility diverges. Our Monte Carlo
simulations yield eta_T simeq 1.515. PV/[NT] = f(eta) and all physical magni-
tudes exhibit a square root branch point at eta = eta_C > eta_T. The MF for
spherical symmetry yields eta_C = 1.561764.. while Monte Carlo on a cube yields
eta_C simeq 1.540.The function f(eta) has a second Riemann sheet which is only
physically realized in the MCE.In the MCE, the collapse phase transition takes
place in this second sheet near eta_MC = 1.26 and the pressure and temperature
are larger in the collapsed phase than in the gas phase.Both collapse phase
transitions (CE and MCE) are of zeroth order since the Gibbs free energy jumps
at the transitions. f(eta), obeys in MF a first order non-linear differential
equation of first kind Abel's type.The MF gives an extremely accurate picture
in agreement with Monte Carlo both in the CE and MCE.Comment: Latex, 51 pages, 15 .ps figures, to appear in Nucl. Phys.
Chern-Simons Theory for Magnetization Plateaus of Frustrated - Heisenberg model
The magnetization curve of the two-dimensional spin-1/2 -
Heisenberg model is investigated by using the Chern-Simons theory under a
uniform mean-field approximation. We find that the magnetization curve is
monotonically increasing for , where the system under zero
external field is in the antiferromagnetic N\'eel phase. For larger ratios of
, various plateaus will appear in the magnetization curve. In
particular, in the disordered phase, our result supports the existence of the
plateau and predicts a new plateau at .
By identifying the onset ratio for the appearance of the 1/2-plateau
with the boundary between the N\'eel and the spin-disordered phases in zero
field, we can determine this phase boundary accurately by this mean-field
calculation. Verification of these interesting results would indicate a strong
connection between the frustrated antiferromagnetic system and the quantum Hall
system.Comment: RevTeX 4, 4 pages, 3 EPS figure
Phase diagram for a class of spin-half Heisenberg models interpolating between the square-lattice, the triangular-lattice and the linear chain limits
We study the spin-half Heisenberg models on an anisotropic two-dimensional
lattice which interpolates between the square-lattice at one end, a set of
decoupled spin-chains on the other end, and the triangular-lattice Heisenberg
model in between. By series expansions around two different dimer ground states
and around various commensurate and incommensurate magnetically ordered states,
we establish the phase diagram for this model of a frustrated antiferromagnet.
We find a particularly rich phase diagram due to the interplay of magnetic
frustration, quantum fluctuations and varying dimensionality. There is a large
region of the usual 2-sublattice Ne\'el phase, a 3-sublattice phase for the
triangular-lattice model, a region of incommensurate magnetic order around the
triangular-lattice model, and regions in parameter space where there is no
magnetic order. We find that the incommensurate ordering wavevector is in
general altered from its classical value by quantum fluctuations. The regime of
weakly coupled chains is particularly interesting and appears to be nearly
critical.Comment: RevTeX, 15 figure
The Physical Principles of Quantum Mechanics. A critical review
The standard presentation of the principles of quantum mechanics is
critically reviewed both from the experimental/operational point and with
respect to the request of mathematical consistency and logical economy. A
simpler and more physically motivated formulation is discussed. The existence
of non commuting observables, which characterizes quantum mechanics with
respect to classical mechanics, is related to operationally testable
complementarity relations, rather than to uncertainty relations. The drawbacks
of Dirac argument for canonical quantization are avoided by a more geometrical
approach.Comment: Bibliography and section 2.1 slightly improve
Quantum disorder in the two-dimensional pyrochlore Heisenberg antiferromagnet
We present the results of an exact diagonalization study of the spin-1/2
Heisenberg antiferromagnet on a two-dimensional version of the pyrochlore
lattice, also known as the square lattice with crossings or the checkerboard
lattice. Examining the low energy spectra for systems of up to 24 spins, we
find that all clusters studied have non-degenerate ground states with total
spin zero, and big energy gaps to states with higher total spin. We also find a
large number of non-magnetic excitations at energies within this spin gap.
Spin-spin and spin-Peierls correlation functions appear to be short-ranged, and
we suggest that the ground state is a spin liquid.Comment: 7 pages, 11 figures, RevTeX minor changes made, Figure 6 correcte
Solution of generalized fractional reaction-diffusion equations
This paper deals with the investigation of a closed form solution of a
generalized fractional reaction-diffusion equation. The solution of the
proposed problem is developed in a compact form in terms of the H-function by
the application of direct and inverse Laplace and Fourier transforms.
Fractional order moments and the asymptotic expansion of the solution are also
obtained.Comment: LaTeX, 18 pages, corrected typo
High precision Monte Carlo simulations of interfaces in the three-dimensional Ising model: a comparison with the Nambu-Goto effective string model
Motivated by the recent progress in the effective string description of the
interquark potential in lattice gauge theory, we study interfaces with periodic
boundary conditions in the three-dimensional Ising model. Our Monte Carlo
results for the associated free energy are compared with the next-to-leading
order (NLO) approximation of the Nambu-Goto string model. We find clear
evidence for the validity of the effective string model at the level of the NLO
truncation.Comment: 20 pages, 1 figur
Baxter Q-operator and Separation of Variables for the open SL(2,R) spin chain
We construct the Baxter Q-operator and the representation of the Separated
Variables (SoV) for the homogeneous open SL(2,R) spin chain. Applying the
diagrammatical approach, we calculate Sklyanin's integration measure in the
separated variables and obtain the solution to the spectral problem for the
model in terms of the eigenvalues of the Q-operator. We show that the
transition kernel to the SoV representation is factorized into the product of
certain operators each depending on a single separated variable. As a
consequence, it has a universal pyramid-like form that has been already
observed for various quantum integrable models such as periodic Toda chain,
closed SL(2,R) and SL(2,C) spin chains.Comment: 29 pages, 9 figures, Latex styl