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We consider the critical behaviour of long-range $O(n)$ models ($n \ge 0$) on ${\mathbb Z}^d$, with interaction that decays with distance $r$ as $r^{-(d+\alpha)}$, for $\alpha \in (0,2)$.
Some theorems on stable processes
R.M. Blumenthal and R.K. Getoor · 1960
Earlier work this paper cites.
Note on fractional powers of linear operators
T. Kato · 1960
Earlier work this paper cites.
Critical exponents for long-range interactions
M.E. Fisher, S. Ma, and B.G. Nickel · 1972
Earlier work this paper cites.
Wilson-type expansions of critical exponents for long-range interactions
M. Suzuki, Y. Yamazaki, and G. Igarashi · 1972
Earlier work this paper cites.
Critical exponents in 3.99 dimensions
K.G. Wilson and M.E. Fisher · 1972
Earlier work this paper cites.
Recursion relations and fixed points for ferromagnets with long-range interactions
J. Sak · 1973
Earlier work this paper cites.
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P. Collet and J.-P. Eckmann · 1978
Earlier work this paper cites.
A rigorous inequality for the specific heat of an Ising or φ 4 \varphi^{4} ferromagnet
A.D. Sokal · 1979
Earlier work this paper cites.
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A.J. McKane · 1980
Earlier work this paper cites.
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G. Parisi and N. Sourlas · 1980
Earlier work this paper cites.
Functional Analysis
K. Yosida · 1980
Earlier work this paper cites.
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Earlier work this paper cites.
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J. Fröhlich · 1982
Earlier work this paper cites.
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K. Gawȩdzki and A. Kupiainen · 1983
Earlier work this paper cites.
The asymptotic evaluation of a class of path integrals. II
J.M. Luttinger · 1983
Earlier work this paper cites.
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D.J. Amit · 1984
Earlier work this paper cites.
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K. Gawȩdzki and A. Kupiainen · 1984
Earlier work this paper cites.
Asymptotic freedom beyond perturbation theory
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Earlier work this paper cites.
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Earlier work this paper cites.
Massless lattice φ 4 4 \varphi^{4}_{4} theory: Rigorous control of a renormalizable asymptotically free model
K. Gawȩdzki and A. Kupiainen · 1985
Earlier work this paper cites.
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Earlier work this paper cites.
Construction and Borel summability of infrared Φ 4 4 \Phi^{4}_{4} by a phase space expansion
J. Feldman, J. Magnen, V. Rivasseau, and R. Sénéor · 1987
Earlier work this paper cites.
Quantum Physics, A Functional Integral Point of View
J. Glimm and A. Jaffe · 1987
Earlier work this paper cites.
A rigorous control of logarithmic corrections in four dimensional φ 4 \varphi^{4} spin systems. I. Trajectory of effective Hamiltonians
T. Hara · 1987
Earlier work this paper cites.
A rigorous control of logarithmic corrections in four dimensional φ 4 \varphi^{4} spin systems. II. Critical behaviour of susceptibility and correlation length
T. Hara and H. Tasaki · 1987
Earlier work this paper cites.
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M. Aizenman and R. Fernández · 1988
Earlier work this paper cites.
Crossover between field theories with short-range and long-range exchange or correlations
J. Honkonen and M.Yu. Nalimov · 1989
Earlier work this paper cites.
An application of Berezin integration to large deviations
D.C. Brydges and I. Muñoz Maya · 1991
Earlier work this paper cites.
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G.F. Lawler · 1991
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Self-avoiding walk in five or more dimensions. I. The critical behaviour
T. Hara and G. Slade · 1992
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The Self-Avoiding Walk
N. Madras and G. Slade · 1993
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