3,574 research outputs found
Phase Diagram of a 2D Vertex Model
Phase diagram of a symmetric vertex model which allows 7 vertex
configurations is obtained by use of the corner transfer matrix renormalization
group (CTMRG), which is a variant of the density matrix renormalization group
(DMRG). The critical indices of this model are identified as and
.Comment: 2 pages, 5 figures, short not
The Density Matrix Renormalization Group technique with periodic boundary conditions
The Density Matrix Renormalization Group (DMRG) method with periodic boundary
conditions is introduced for two dimensional classical spin models. It is shown
that this method is more suitable for derivation of the properties of infinite
2D systems than the DMRG with open boundary conditions despite the latter
describes much better strips of finite width. For calculation at criticality,
phenomenological renormalization at finite strips is used together with a
criterion for optimum strip width for a given order of approximation. For this
width the critical temperature of 2D Ising model is estimated with seven-digit
accuracy for not too large order of approximation. Similar precision is reached
for critical indices. These results exceed the accuracy of similar calculations
for DMRG with open boundary conditions by several orders of magnitude.Comment: REVTeX format contains 8 pages and 6 figures, submitted to Phys. Rev.
Phase Transition of the Ising model on a Hyperbolic Lattice
The matrix product structure is considered on a regular lattice in the
hyperbolic plane. The phase transition of the Ising model is observed on the
hyperbolic lattice by means of the corner-transfer-matrix
renormalization group (CTMRG) method. Calculated correlation length is always
finite even at the transition temperature, where mean-field like behavior is
observed. The entanglement entropy is also always finite.Comment: 4 pages, 3 figure
Implication of Compensator Field and Local Scale Invariance in the Standard Model
We introduce Weyl's scale symmetry into the standard model (SM) as a local
symmetry. This necessarily introduces gravitational interactions in addition to
the local scale invariance group \tilde U(1) and the SM groups SU(3) X SU(2) X
U(1). The only other new ingredients are a new scalar field \sigma and the
gauge field for \tilde U(1) we call the Weylon. A noteworthy feature is that
the system admits the St\" uckelberg-type compensator. The \sigma couples to
the scalar curvature as (-\zeta/2) \sigma^2 R, and is in turn related to a St\"
uckelberg-type compensator \varphi by \sigma \equiv M_P e^{-\varphi/M_P} with
the Planck mass M_P. The particular gauge \varphi = 0 in the St\" uckelberg
formalism corresponds to \sigma = M_P, and the Hilbert action is induced
automatically. In this sense, our model presents yet another mechanism for
breaking scale invariance at the classical level. We show that our model
naturally accommodates the chaotic inflation scenario with no extra field.Comment: This work is to be read in conjunction with our recent comments
hep-th/0702080, arXiv:0704.1836 [hep-ph] and arXiv:0712.2487 [hep-ph]. The
necessary ingredients for describing chaotic inflation in the SM as
entertained by Bezrukov and Shaposhnikov [17] have been provided by our
original model [8]. We regret their omission in citing our original model [8
Chiral Reductions in the Salam-Sezgin Model
Reductions from six to four spacetime dimensions are considered for a class
of supergravity models based on the six-dimensional Salam-Sezgin model, which
is a chiral theory with a gauged U(1) R-symmetry and a positive scalar-field
potential. Reduction on a sphere and monopole background of such models
naturally yields four-dimensional theories without a cosmological constant. The
question of chirality preservation in such a reduction has been a topic of
debate. In this article, it is shown that the possibilities of dimensional
reduction bifurcate into two separate consistent dimensional-reduction schemes.
One of these retains the massless SU(2) vector gauge triplet arising from the
sphere's isometries, but it produces a non-chiral four-dimensional theory. The
other consistent scheme sets to zero the SU(2) gauge fields, but retains the
gauged U(1) from six dimensions and preserves chirality although the U(1) is
spontaneously broken. Extensions of the Salam-Sezgin model to include larger
gauge symmetries produce genuinely chiral models with unbroken gauge
symmetries.Comment: 37 page
The Signature Triality of Majorana-Weyl Spacetimes
Higher dimensional Majorana-Weyl spacetimes present space-time dualities
which are induced by the Spin(8) triality automorphisms. Different signature
versions of theories such as 10-dimensional SYM's, superstrings, five-branes,
F-theory, are shown to be interconnected via the S_3 permutation group.
Bilinear and trilinear invariants under space-time triality are introduced and
their possible relevance in building models possessing a space-versus-time
exchange symmetry is discussed. Moreover the Cartan's ``vector/chiral
spinor/antichiral spinor" triality of SO(8) and SO(4,4) is analyzed in detail
and explicit formulas are produced in a Majorana-Weyl basis. This paper is the
extended version of hep-th/9907148.Comment: 28 pages, LaTex. Extended version of hep-th/990714
Macroscopic nucleation phenomena in continuum media with long-range interactions
Nucleation, commonly associated with discontinuous transformations between
metastable and stable phases, is crucial in fields as diverse as atmospheric
science and nanoscale electronics. Traditionally, it is considered a
microscopic process (at most nano-meter), implying the formation of a
microscopic nucleus of the stable phase. Here we show for the first time, that
considering long-range interactions mediated by elastic distortions, nucleation
can be a macroscopic process, with the size of the critical nucleus
proportional to the total system size. This provides a new concept of
"macroscopic barrier-crossing nucleation". We demonstrate the effect in
molecular dynamics simulations of a model spin-crossover system with two
molecular states of different sizes, causing elastic distortions.Comment: 12 pages, 4 figures. Supplementary information accompanies this paper
at http://www.nature.com/scientificreport
Critical exponents of the two-layer Ising model
The symmetric two-layer Ising model (TLIM) is studied by the corner transfer
matrix renormalisation group method. The critical points and critical exponents
are calculated. It is found that the TLIM belongs to the same universality
class as the Ising model. The shift exponent is calculated to be 1.773, which
is consistent with the theoretical prediction 1.75 with 1.3% deviation.Comment: 7 pages, with 10 figures include
Dilaton and Second-Rank Tensor Fields as Supersymmetric Compensators
We formulate a supersymmetric theory in which both a dilaton and a
second-rank tensor play roles of compensators. The basic off-shell multiplets
are a linear multiplet (B_{\mu\nu}, \chi, \phi) and a vector multiplet (A_\mu,
\l; C_{\mu\nu\rho}), where \phi and B_{\m\n} are respectively a dilaton and a
second-rank tensor. The third-rank tensor C_{\mu\nu\rho} in the vector
multiplet is 'dual' to the conventional D-field with 0 on-shell or 1 off-shell
degree of freedom. The dilaton \phi is absorbed into one longitudinal component
of A_\mu, making it massive. Initially, B_{\mu\nu} has 1 on-shell or 3
off-shell degrees of freedom, but it is absorbed into the longitudinal
components of C_{\mu\nu\rho}. Eventually, C_{\mu\nu\rho} with 0 on-shell or 1
off-shell degree of freedom acquires in total 1 on-shell or 4 off-shell degrees
of freedom, turning into a propagating massive field. These basic multiplets
are also coupled to chiral multiplets and a supersymmetric Dirac-Born-Infeld
action. Some of these results are also reformulated in superspace. The proposed
mechanism may well provide a solution to the long-standing puzzle of massless
dilatons and second-rank tensors in supersymmetric models inspired by string
theory.Comment: 15 pages, no figure
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