Introduction to Conformal Invariance and Its Applications to Critical Phenomena

Correlation Functions in a Corner-Shaped Ising Model

“…In this two-dimensional Fourier transform the only factors coupling the two integration variables are ͑z 1 2 z 2 ͒ 21 and ͑z 1 z 2 2 1͒ 21 coming from (12) or (13). This suggests the introduction of a "lattice second derivative"…”

“…1. Comparison of g lc ͑1, j͒ constructed from the conformal result (thick lines) with the exact critical correlation function g͑1, j͒ (points) obtained by numerical integration of (14) with (12) or (13) 2͒], and A ͑iii͒ `(the extreme anisotropic or Hamiltonian limit K 2 ø K 1 ).…”

Scale Symmetry in the Universe

“…This situation is common, for example, in critical phenomena in statistical physics, in which it is called crossover. The theory of critical phenomena is actually a fruitful domain of application of the theory of scale invariance and furthermore of the full theory of conformal invariance [16]. The purpose of the present paper is to study the theory of the fractal structure of the universe with methods of statistical physics and field theory.…”

Transições de fase.

“…Um grande avanço que merece ser mencionado, mas que não será abordado nesta resenha,é a teoria de invariância conforme que permitiu um en-tendimento bem mais profundo de muitos modelos clássicos bidimensionais e modelos quânticos unidimensionais, veja, por exemplo, as refs. [22] e [23]. Outra omissão refere-seà teoria das transições de fase de primeira ordem.…”

“…23) onde, k 1 +k 2 +k 3 = 0. Para calcular o diagrama basta conhecer o propagador livre, G(k), e as expressões entre colchetes que representam os diagramas de 3 pernas (triângulo), e o de 2 pernas (oval), sem os propagadores G(k) nas linhas externas.…”