23 research outputs found
Dimensional Reduction by Conformal Bootstrap
The dimensional reductions in the branched polymer and the random field Ising
model (RFIM) are discussed by a conformal bootstrap method. The small size
minors are applied for the evaluations of the scale dimensions of these two
models and the results are compared to D'=D-2 dimensional Yang-Lee edge
singularity and to pure D'=D-2 dimensional Ising model, respectively. For the
former case, the dimensional reduction is shown to be valid for , and for the latter case, the deviation from the dimensional reduction can
be seen below five dimensions.Comment: 23 page, 13 figure
Punctures and p-spin curves from matrix models III. Dl type and logarithmic potential
The intersection numbers for p spin curves of the moduli space M(g,n) are
considered for D type by a matrix model. The asymptotic behavior of the large
genus g limit and large p limit are derived. The remarkable features of the
cases of p= 1/2, - 1/2, -2, -3 are examined in the Laurent expansion for
multiple correlation functions. The strong coupling expansions for the negative
p cases are considered.Comment: 40 page
Spectral Form Factor for Time-dependent Matrix model
The quantum chaos is related to a Gaussian random matrix model, which shows a
dip-ramp-plateau behavior in the spectral form factor for the large size .
The spectral form factor of time dependent Gaussian random matrix model shows
also dip-ramp-plateau behavior with a rounding behavior instead of a kink near
Heisenberg time. This model is converted to two matrix model, made of and
. The numerical evaluation for finite and analytic expression in the
large are compared for the spectral form factor.Comment: 38 pages,16 figure
Instanton and Superconductivity in Supersymmetric CP(N-1) Model
The two dimensional supersymmetric CP(N-1) model has a striking similarity to
the N=2 supersymmetric gauge theory in four dimensions. The BPS mass formula
and the curve of the marginal stability (CMS), which exist in the four
dimensional gauge theory, appears in this two dimensional CP(N-1) model. These
two quntities are derived by a one-dimensional n-vector spin model in the large
n limit for the N=2 case. This mapping is further investigated at the critical
point. An application of the study of the BPS mass formula is proposed to the
phenomena of the spin and charge separations in the Higgs phase.Comment: 6 page
Exponent of n-Ising matter fields coupled to 2d gravity
n-Ising spins on a random surface represented by a matrix model is studied as
a model of the 2D gravity coupled to matter field with the central charge c >
1. The magnetic field is introduced to discuss the scaling exponent ,
and the value of this magnetic field exponent is estimated by the series
expansion.Comment: 9page
Logarithmic moments of characteristic polynomials of random matrices
In a recent article we have discussed the connections between averages of
powers of Riemann's -function on the critical line, and averages of
characteristic polynomials of random matrices. The result for random matrices
was shown to be universal, i.e. independent of the specific probability
distribution, and the results were derived for arbitrary moments. This allows
one to extend the previous results to logarithmic moments, for which we derive
the explicit universal expressions in random matrix theory. We then compare
these results to various results and conjectures for -functions, and the
correspondence is again striking.Comment: 10 pages, late
Perturbative analysis of an n-Ising model on a random surface
Two dimensional quantum gravity coupled to a conformally invariant matter
field of central charge c=n/2, is represented, in a discretized version, by n
independent Ising spins per cell of the triangulations of a random surface. The
matrix integral representation of this model leads to a diagrammatic expansion
at large orders, when the Ising coupling constant is tuned to criticality, one
extracts the values of the string susceptibility exponent. We extend our
previous calculation to order eight for genus zero and investigate now also the
genus one case in order to check the possibility of having a well-defined
double scaling limit even c>1.Comment: 9p