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Abstract: For classical lattice systems with finite (Ising) spins, we show that the implementation of momentum-space renormalization at the level of Hamiltonians runs into the same type of difficulties as found for real-space transformations: Renormalized Hamiltonians are ill-defined in certain regions of the phase diagram. PACS: 64.60Ak, 05.50+q, 02.50Cv 1 Introduction Despite the great success of renormalization-group (RG) ideas, both for computations and as a heuristic guide, many aspects of... (Update)
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BibTeX entry: (Update)
A. C. D. van Enter and R. Fern'andez. Problems with the definition of renormalized Hamiltonians of momentum-space renormalization transformations. In preparation. http://citeseer.ist.psu.edu/vanenter98problems.html More
@misc{ enter-problems,
author = "A. van Enter and R. Fern'andez",
title = "Problems with the definition of renormalized Hamiltonians of momentum-space
renormalization transformations",
text = "A. C. D. van Enter and R. Fern'andez. Problems with the definition of renormalized
Hamiltonians of momentum-space renormalization transformations. In preparation.",
url = "citeseer.ist.psu.edu/vanenter98problems.html" }
Citations (may not include all citations):40 Lectures on Phase Transitions and the Renormalization Group (context) - Goldenfeld - 1992
31 Theory of Phase Transitions: Rigorous Results (context) - Sinai - 1982
27 Regularity properties and pathologies of position-space reno.. (context) - van Enter, Fern'andez et al. - 1993
25 Mathematical properties of position-space renormalization-gr.. (context) - Griffiths, Pearce - 1979
23 Probability and Physics (context) - Dobrushin, representation et al. - 1995
19 Renormalization group pathologies and the definition of Gibb.. - Bricmont, Kupiainen et al. - 1998
14 Position-space renormalization-group transformations: Some p.. (context) - Griffiths, Pearce - 1978
13 Princeton University Press (context) - Benfatto, Gallavotti et al. - 1995
11 the possible failure of the Gibbs property for measures on l.. - van Enter - 1996
11 The renormalization group and the ffl-expansion (context) - Wilson, Kogut - 1974
9 Pathological behavior of renormalization-group maps at high .. - van Enter, Fern'andez et al. - 1995
9 Peierls condition and the number of ground states (context) - Holsztynski, Slawny - 1978
9 Ill-defined block-spin transformations at arbitrarily high t.. - van Enter - 1996
7 Singular renormalization group transformations and first ord.. (context) - Hasenfratz, Hasenfratz - 1988
6 Weakly Gibbsian measures for lattice spin systems - Lorinczi, Maes - 1997
6 Renormalization transformations in the vicinity of first-ord.. (context) - van Enter, Fern'andez et al. - 1991
6 Private communication (context) - Fisher - 1992
5 Coarse graining approach to first order phase transitions (context) - Gawedzki, Koteck'y et al. - 1987
4 Introduction to the Renormalization Group and to Critical Ph.. (context) - Pfeuty, Toulouse - 1977
4 Renormalization theory for Isinglike spin systems (context) - Niemeijer, van Leeuwen - 1976
4 Mathematical properties of renormalization-group transformat.. (context) - Griffiths - 1981
3 A remark on different norms and analyticity for many-particl.. (context) - van Enter, Fern'andez - 1989
2 A rigorous block spin approach to massless lattice theories (context) - Gawedzki, Kupiainen - 1980
2 To appear in Commun (context) - Dobrushin, Shlosman - 1998
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