scholarly journals THE CRITICAL POINT OF UNORIENTED RANDOM SURFACES WITH A NONEVEN POTENTIAL

1993 ◽  
Vol 08 (06) ◽  
pp. 1139-1152
Author(s):  
M.A. MARTÍN-DELGADO
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Critical Point ◽  
Discrete Model ◽  
Recursion Relation ◽  
Scaling Limit ◽  
Random Surfaces ◽  
Matrix Ensemble ◽  
Quartic Interaction ◽  
Double Scaling Limit

The discrete model of the real symmetric one-matrix ensemble is analyzed with a cubic interaction. The partition function is found to satisfy a recursion relation that solves the model. The double scaling-limit of the recursion relation leads to a Miura transformation relating the contributions to the free energy coming from oriented and unoriented random surfaces. This transformation is the same kind as found with a quartic interaction.

scholarly journals SUPERLOOP EQUATIONS AND TWO-DIMENSIONAL SUPERGRAVITY

1992 ◽  
Vol 07 (21) ◽  
pp. 5337-5367 ◽  
Author(s):  
L. ALVAREZ-GAUMÉ ◽  
H. ITOYAMA ◽  
J.L. MAÑES ◽  
A. ZADRA
Keyword(s):  
Partition Function ◽  
Discrete Model ◽  
Continuum Limit ◽  
Basic Assumption ◽  
Scaling Limit ◽  
Integrable Hierarchy ◽  
Two Dimensional ◽  
Virasoro Constraints ◽  
Double Scaling Limit ◽  
The Continuum

We propose a discrete model whose continuum limit reproduces the string susceptibility and the scaling dimensions of (2, 4m) minimal superconformal models coupled to 2D supergravity. The basic assumption in our presentation is a set of super-Virasoro constraints imposed on the partition function. We recover the Neveu-Schwarz and Ramond sectors of the theory, and we are also able to evaluate all planar loop correlation functions in the continuum limit. We find evidence to identify the integrable hierarchy of nonlinear equations describing the double scaling limit as a supersymmetric generalization of KP studied by Rabin.

scholarly journals NON-PERTURBATIVE SOLUTION OF THE SUPER-VIRASORO CONSTRAINTS

1993 ◽  
Vol 08 (13) ◽  
pp. 1205-1214 ◽  
Author(s):  
K. BECKER ◽  
M. BECKER
Keyword(s):  
Partition Function ◽  
Matrix Model ◽  
Scaling Limit ◽  
Virasoro Constraints ◽  
Perturbative Solution ◽  
The One ◽  
Genus Expansion ◽  
Double Scaling Limit

We present the solution of the discrete super-Virasoro constraints to all orders of the genus expansion. Integrating over the fermionic variables we get a representation of the partition function in terms of the one-matrix model. We also obtain the non-perturbative solution of the super-Virasoro constraints in the double scaling limit but do not find agreement between our flows and the known supersymmetric extensions of KdV.

scholarly journals MATRIX MODELS AND INTEGRABLE C<1 OPEN STRING THEORIES

1994 ◽  
Vol 03 (01) ◽  
pp. 203-206
Author(s):  
LAURENT HOUART
Keyword(s):  
Ising Model ◽  
Boundary Conditions ◽  
Matrix Models ◽  
Matrix Model ◽  
Scaling Limit ◽  
Open String ◽  
String Equation ◽  
Random Surfaces ◽  
Ising Spins ◽  
Double Scaling Limit

We study in the double scaling limit the two-matrix model which represents the sum over closed and open random surfaces coupled to an Ising model. The boundary conditions are characterized by the fact that the Ising spins sitting at the vertices of the boundaries are all in the same state. We obtain the string equation.

scholarly journals INTERACTION HIERARCHY: STRING AND QUANTUM GRAVITY

1996 ◽  
Vol 11 (17) ◽  
pp. 1379-1396 ◽  
Author(s):  
G.K. SAVVIDY ◽  
K.G. SAVVIDY
Keyword(s):  
Partition Function ◽  
Quantum Gravity ◽  
Spin System ◽  
Scaling Limit ◽  
Functional Integral ◽  
Local Interaction ◽  
Linear Action ◽  
Random Surfaces

We have found that the functional integral for quantum gravity can be represented as a superposition of less complicated theory of random surfaces with Euler character as an action. We propose an alternative linear action A(M4) for quantum gravity. On the lattice we constructed spin system with local interaction, which has the equivalent partition function. The scaling limit is discussed.

Critical Properties of Isobaric Processes of Lennard-Jones Gases

2005 ◽  
Vol 60 (1-2) ◽  
pp. 23-28
Author(s):  
Akira Matsumoto
Keyword(s):  
Heat Capacity ◽  
Free Energy ◽  
Partition Function ◽  
Critical Point ◽  
Gibbs Free Energy ◽  
Canonical Ensemble ◽  
Thermodynamic Quantities ◽  
Lennard Jones ◽  
The Laplace Transform ◽  
Enthalpy And Entropy

The thermodynamic quantities of Lennard-Jones gases, evaluated till the fourth virial coefficient, are investigated for an isobaric process. A partition function in the T-P grand canonical ensemble Y(T,P,N) may be defined by the Laplace transform of the partition function Z(T,V,N) in the canonical ensemble. The Gibbs free energy is related with Y(T,P,N) by the Legendre transformation G(T,P,N) = −kT logY(T,P,N). The volume, enthalpy, entropy, and heat capacity are analytically expressed as functions of the intensive variables temperature and pressure. Some critical thermodynamic quantities for Xe are calculated and drawn. At the critical point the heat capacity diverges to infinity, while the Gibbs free energy, volume, enthalpy, and entropy are continuous. This suggests that a second-order phase transition may occur at the critical point.

THE PENNER MATRIX MODEL AND c = 1 STRINGS

1991 ◽  
Vol 06 (18) ◽  
pp. 1665-1677 ◽  
Author(s):  
S. CHAUDHURI ◽  
H. DYKSTRA ◽  
J. LYKKEN
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
Matrix Model ◽  
Critical Radius ◽  
Scaling Limit ◽  
Legendre Transform ◽  
Complex Eigenvalue ◽  
Closed Contour ◽  
Branch Points ◽  
Double Scaling Limit

The steepest descent solution of the Penner matrix model has a one-cut eigenvalue support. Criticality results when the two branch points of this support coalesce. The support is then a closed contour in the complex eigenvalue plane. Simple generalizations of the Penner model have multi-cut solutions. For these models, the eigenvalue support at criticality is also a closed contour, but consisting of several cuts. We solve the simplest such model, which we call the KT model, in the double-scaling limit. Its free energy is a Legendre transform of the free energy of the c = 1 string compactified to the critical radius of the Kosterlitz–Thouless phase transition.

scholarly journals SCALING VIOLATION IN O(N) VECTOR MODELS

1994 ◽  
Vol 09 (07) ◽  
pp. 631-641 ◽  
Author(s):  
SHINSUKE NISHIGAKI
Keyword(s):  
Free Energy ◽  
Random Walk ◽  
Vector Field ◽  
Cayley Tree ◽  
Scaling Limit ◽  
Field Theories ◽  
One Dimension ◽  
Polymeric Systems ◽  
N Vector ◽  
Double Scaling Limit

We investigate O(N)-symmetric vector field theories in the double scaling limit. Our model describes branched polymeric systems in D dimensions, whose multicritical series interpolates between the Cayley tree and the ordinary random walk. We give explicit forms of residual divergences in the free energy, analogous to those observed in the strings in one dimension.

scholarly journals SOLUTION OF MATRIX MODELS IN THE D III GENERATOR ENSEMBLE

1994 ◽  
Vol 09 (19) ◽  
pp. 3339-3351
Author(s):  
HAROLD ROUSSEL
Keyword(s):  
Free Energy ◽  
Matrix Models ◽  
Scaling Limit ◽  
New Techniques ◽  
Matrix Ensembles ◽  
Double Scaling Limit

In this work we solve two new matrix models using standard and new techniques. The two models are based on matrix ensembles not previously considered, namely the D III generator ensemble. It is shown that, in the double scaling limit, their free energy has the same behavior as previous models describing oriented and unoriented surfaces. We also found an additional solution for one of the models.

DOUBLE SCALING LIMIT IN O(N) VECTOR MODELS IN D DIMENSIONS

1992 ◽  
Vol 07 (07) ◽  
pp. 1391-1413 ◽  
Author(s):  
P. DI VECCHIA ◽  
M. KATO ◽  
N. OHTA
Keyword(s):  
Partition Function ◽  
Matrix Models ◽  
Scaling Limit ◽  
Coupling Constant ◽  
Polymer Model ◽  
Critical Theories ◽  
A Value ◽  
Arbitrary Potential ◽  
N Vector ◽  
Double Scaling Limit

Using the standard 1/N expansion, we study O(N) vector models in D dimensions with an arbitrary potential. We limit ourselves to renormalizable theories. We show that there exists a value of the coupling constant corresponding to a critical point and that a double scaling limit can be performed as in D=0 and in the case of matrix models in D=0, 1. For D=1 the theory is renormalizable with an arbitrary potential and we find in general a hierarchy of critical theories labeled by an integer k. The universal partition function obtained in the double scaling limit is constructed. Finally, we show that the critical behaviour of those models is the same as a branched polymer model recently constructed by Ambjørn, Durhuus and Jónsson.

scholarly journals CONCERNING THE DOUBLE SCALING LIMIT IN THE O(N) VECTOR MODEL IN FOUR DIMENSIONS

1992 ◽  
Vol 07 (26) ◽  
pp. 2449-2452 ◽  
Author(s):  
HOWARD J. SCHNITZER
Keyword(s):  
Critical Point ◽  
Effective Potential ◽  
Scaling Limit ◽  
Vector Model ◽  
Four Dimensions ◽  
N Vector ◽  
Double Scaling Limit

The 1/N expansion for the O(N) vector model in four dimensions is reconsidered. It is emphasized that the effective potential for this model becomes everywhere complex just at the critical point, which signals an unstable vacuum. Thus a critical O(N) vector model cannot be consistently defined in the 1/N expansion for four dimensions, which makes the existence of a double-scaling limit for this theory doubtful.

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