81 research outputs found
Universal amplitude ratios and Coxeter geometry in the dilute A model
The leading excitations of the dilute model in regime 2 are considered
using analytic arguments. The model can be identified with the integrable
perturbation of the unitary minimal series . It is
demonstrated that the excitation spectrum of the transfer matrix satisfies the
same functional equations in terms of elliptic functions as the exact
S-matrices of the perturbation do in terms of trigonometric
functions. In particular, the bootstrap equation corresponding to a self-fusing
process is recovered. For the special cases corresponding to the
Ising model in a magnetic field, and the leading thermal perturbations of the
tricritical Ising and three-state Potts model, as well as for the unrestricted
model, , we relate the structure of the Bethe roots to the Lie
algebras and using Coxeter geometry. In these cases Coxeter
geometry also allows for a single formula in generic Lie algebraic terms
describing all four cases. For general we calculate the spectral gaps
associated with the leading excitation which allows us to compute universal
amplitude ratios characteristic of the universality class. The ratios are of
field theoretic importance as they enter the bulk vacuum expectation value of
the energy momentum tensor associated with the corresponding integrable quantum
field theories.Comment: 32 pages (tcilatex
The dilute A model, the E mass spectrum and the tricritical Ising model
The exact perturbation approach is used to derive the (seven) elementary
correlation lengths and related mass gaps of the two-dimensional dilute A
lattice model in regime 2- from the Bethe ansatz solution. This model provides
a realisation of the integrable perturbation of the c=7/10
conformal field theory, which is known to describe the off-critical thermal
behaviour of the tricritical Ising model. The E masses predicted from
purely elastic scattering theory follow in the approach to criticality.
Universal amplitudes for the tricritical Ising model are calculated.Comment: 24 pages, LaTeX, submitted to Journal of Mathematical Physics. One
paragraph added and some minor typos correcte
Ising tricriticality and the dilute A model
Some universal amplitude ratios appropriate to the peturbation
of the c=7/10 minimal field theory, the subleading magnetic perturbation of the
tricritical Ising model, are explicitly demonstrated in the dilute A model,
in regime 1.Comment: 8 pages, LaTeX using iop macro
Correlation lengths and E_8 mass spectrum of the dilute A_3 lattice model
The exact perturbation approach is used to derive the elementary correlation
lengths and related mass gaps of the two-dimensional dilute A_L
lattice model in regimes 1 and 2 for L odd from the Bethe Ansatz solution. In
regime 2 the A_3 model is the E_8 lattice realisation of the two-dimensional
Ising model in a magnetic field at T=T_c. The calculations for the A_3 model in
regime 2 start from the eight thermodynamically significant string types found
in previous numerical studies. These string types are seen to be consistent in
the ordered high field limit. The eight masses obtained reduce with the
approach to criticality to the E_8 masses predicted by Zamolodchikov, thus
providing a further direct lattice determination of the E_8 mass spectrum.Comment: 57 pages, Latex, Elsevier style file
Expanding depth and meaning within urban design processes through the application of complexity and evolutionary theories
Previous research has established the value of regarding cities as complex systems, and as systems which will evolve over time. The research reported in this paper concerns the development of an approach to urban design and management which recognises the complexities of change resulting from design-led urban interventions. The research commenced with a study of urban design and urban management processes, and the manner in which they have been studied in an academic context. The system aims to guide the processes of urban design so that it can be implemented within a cyclical process of evaluation and application. The system aids communication across design teams and improves clarity within the design process for the designers themselves. The specific system also aspires to interconnect theory with practice, while supporting designers to be inclusive and holistic. The paper describes a case study where the framework was applied within an academic setting, related to real urban environments in Singapore. It validates the modelâs ability to guide students through the design process, give depth to their analysis of urban systems and meaning to their designs. Action research was implemented, to reflect the need for a âpractice-changing practiceâ methodology, that supports a greater understanding of the relationship between theory and practice
Magnetic Correlation Length and Universal Amplitude of the Lattice E_8 Ising Model
The perturbation approach is used to derive the exact correlation length
of the dilute A_L lattice models in regimes 1 and 2 for L odd. In regime
2 the A_3 model is the E_8 lattice realisation of the two-dimensional Ising
model in a magnetic field h at T=T_c. When combined with the singular part f_s
of the free energy the result for the A_3 model gives the universal amplitude
as in precise agreement with the result
obtained by Delfino and Mussardo via the form-factor bootstrap approach.Comment: 7 pages, Late
Off-Critical Logarithmic Minimal Models
We consider the integrable minimal models , corresponding
to the perturbation off-criticality, in the {\it logarithmic
limit\,} , where are coprime and the
limit is taken through coprime values of . We view these off-critical
minimal models as the continuum scaling limit of the
Forrester-Baxter Restricted Solid-On-Solid (RSOS) models on the square lattice.
Applying Corner Transfer Matrices to the Forrester-Baxter RSOS models in Regime
III, we argue that taking first the thermodynamic limit and second the {\it
logarithmic limit\,} yields off-critical logarithmic minimal models corresponding to the perturbation of the critical
logarithmic minimal models . Specifically, in accord with the
Kyoto correspondence principle, we show that the logarithmic limit of the
one-dimensional configurational sums yields finitized quasi-rational characters
of the Kac representations of the critical logarithmic minimal models . We also calculate the logarithmic limit of certain off-critical
observables related to One Point Functions and show that the
associated critical exponents
produce all conformal dimensions in the infinitely extended Kac table. The corresponding Kac labels
satisfy . The exponent is obtained from the logarithmic limit of the free energy giving the
conformal dimension for the perturbing field . As befits a non-unitary
theory, some observables diverge at criticality.Comment: 18 pages, 5 figures; version 3 contains amplifications and minor
typographical correction
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