Finite Size Dependence of the Free Energy in Two-dimensional Critical Systems

Cardy, John L.; Peschel, Ingo

doi:10.1016/0550-3213(88)90604-9

Finite Size Dependence of the Free Energy in Two-dimensional Critical Systems

John L. Cardy
(
- UC, Santa Barbara
)
,
Ingo Peschel
(
- UC, Santa Barbara
)

Apr 11, 1988

16 pages

Published in:

Nucl.Phys.B 300 (1988) 377-392

Published: 1988

DOI:

10.1016/0550-3213(88)90604-9

Report number:

UCSB-TH-88-1988

View in:

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Abstract: (Elsevier)

We show that the free energy at criticality of a finite two-dimensional system of characteristic size L has in general a term which behaves like ln L as L → ∞. The coefficient of this term is universal and is proportional to the conformal anomaly number c . Furthermore, when the metric is non-singular and the boundaries are smooth, this coefficient depends only on the topology and is equal to − 1 6 c gX , where Ξ is the Euler characteristic. However, if there are conical singularities in the metric, or corners on the boundary, this is no longer true. For these cases, we give the correct result.

FIELD THEORY: TWO-DIMENSIONAL
FIELD THEORY: CRITICAL PHENOMENA
FIELD THEORY: FINITE SIZE
FIELD THEORY: SPACE-TIME
ANOMALY: CONFORMAL
TENSOR: ENERGY-MOMENTUM
STATISTICAL MECHANICS: TRANSFER MATRIX
FIELD THEORY: SCALAR
LATTICE FIELD THEORY
TRANSFORMATION: CONFORMAL

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