10,111 research outputs found
Random and aperiodic quantum spin chains: A comparative study
According to the Harris-Luck criterion the relevance of a fluctuating
interaction at the critical point is connected to the value of the fluctuation
exponent omega. Here we consider different types of relevant fluctuations in
the quantum Ising chain and investigate the universality class of the models.
At the critical point the random and aperiodic systems behave similarly, due to
the same type of extreme broad distribution of the energy scales at low
energies. The critical exponents of some averaged quantities are found to be a
universal function of omega, but some others do depend on other parameters of
the distribution of the couplings. In the off-critical region there is an
important difference between the two systems: there are no Griffiths
singularities in aperiodic models.Comment: 4 pages RevTeX, 2 eps-figures include
Recent Progress in Spin Glasses
We review recent findings on spin glass models. Both the equilibrium
properties and the dynamic properties are covered. We focus on progress in
theoretical, in particular numerical, studies, while its relationship to real
magnetic materials is also mentioned.Comment: Chapter 6 in ``Frustrated Spin Systems'' edited by H.T.Die
Application of a continous time cluster algorithm to the Two-dimensional Random Quantum Ising Ferromagnet
A cluster algorithm formulated in continuous (imaginary) time is presented
for Ising models in a transverse field. It works directly with an infinite
number of time-slices in the imaginary time direction, avoiding the necessity
to take this limit explicitly. The algorithm is tested at the zero-temperature
critical point of the pure two-dimensional (2d) transverse Ising model. Then it
is applied to the 2d Ising ferromagnet with random bonds and transverse fields,
for which the phase diagram is determined. Finite size scaling at the quantum
critical point as well as the study of the quantum Griffiths-McCoy phase
indicate that the dynamical critical exponent is infinite as in 1d.Comment: 4 pages RevTeX, 3 eps-figures include
The One-Dimensional ANNNI model in a Transverse Field: Analytic and numerical study of Effective Hamiltonians
We consider a spin- chain with competing nearest and
next-nearest neighbor interactions within a transverse magnetic field, which is
known to be an equiavelent to the ANNNI model. When studing thermodynamics of
the 2D ANNNI model Villain and Bak arrived to a free fermion approximation that
neglects heavy excitations from the ferromagnetic ground state, which is an
appropriate description close to the paramagnetic-ferromagnetic transition. In
the vicinity of the floating-phase/anti-phase transition another sort of
quasiparticles, but free fermions too, appears to be convenient. Although free
fermions are a suitable tool for investigation of the phase diagram and the
critical properties, they are defined on the fictitious lattice which makes the
analysis non-rigorous. Here we deal with a proper fermion scheme which is
especially effective %devised to describe the floating-phase/anti-phase
transition. for performing exact diagonalization calculations for cyclic
chains. Systems up to size has been analysed and the predictions of the
effective fermion Hamiltonian has been confirmed. Various predictions for the
infinite system and the critical properties are derived.Comment: 30 RevTeX pages, 10 postscript figure
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