Pathological Behavior of Renormalization-Group Maps at High Fields and Above the Transition Temperature

Aernout C.D. van Enter; Roberto Fernández; Roman Kotecký

Pathological Behavior of Renormalization-Group Maps at High Fields and Above the Transition Temperature

Aernout C.D. van Enter, Roberto Fernández, Roman Kotecký

Research output: Contribution to journal › Article › Academic › peer-review

24 Citations (Scopus)

Abstract

We show that decimation transformations applied to high-q Potts models result in non-Gibbsian measures even for temperatures higher than the transition temperature. We also show that majority transformations applied to the Ising model in a very strong field at low temperatures produce non-Gibbsian measures. This shows that pathological behavior of renormalization-group transformations is even more widespread than previous examples already suggested.

Original language	English
Pages (from-to)	969-992
Number of pages	24
Journal	Journal of Statistical Physics
Volume	79
Issue number	5-6
Publication status	Published - Jun-1995

Keywords

NON-GIBBSIAN MEASURES
REAL-SPACE RENORMALIZATION
COMPLETE ANALYTICITY
MAJORITY-RULE
DECIMATION
1ST-ORDER PHASE-TRANSITIONS
GROUP TRANSFORMATIONS
LATTICE

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title = "Pathological Behavior of Renormalization-Group Maps at High Fields and Above the Transition Temperature",

abstract = "We show that decimation transformations applied to high-q Potts models result in non-Gibbsian measures even for temperatures higher than the transition temperature. We also show that majority transformations applied to the Ising model in a very strong field at low temperatures produce non-Gibbsian measures. This shows that pathological behavior of renormalization-group transformations is even more widespread than previous examples already suggested.",

keywords = "NON-GIBBSIAN MEASURES, REAL-SPACE RENORMALIZATION, COMPLETE ANALYTICITY, MAJORITY-RULE, DECIMATION, 1ST-ORDER PHASE-TRANSITIONS, GROUP TRANSFORMATIONS, LATTICE",

author = "Enter, {Aernout C.D. van} and Roberto Fern{\'a}ndez and Roman Koteck{\'y}",

note = "Relation: http://www.rug.nl/informatica/organisatie/overorganisatie/iwi Rights: University of Groningen. Research Institute for Mathematics and Computing Science (IWI)",

year = "1995",

month = jun,

language = "English",

volume = "79",

pages = "969--992",

journal = "Journal of Statistical Physics",

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T1 - Pathological Behavior of Renormalization-Group Maps at High Fields and Above the Transition Temperature

AU - Enter, Aernout C.D. van

AU - Fernández, Roberto

AU - Kotecký, Roman

N1 - Relation: http://www.rug.nl/informatica/organisatie/overorganisatie/iwi Rights: University of Groningen. Research Institute for Mathematics and Computing Science (IWI)

PY - 1995/6

Y1 - 1995/6

N2 - We show that decimation transformations applied to high-q Potts models result in non-Gibbsian measures even for temperatures higher than the transition temperature. We also show that majority transformations applied to the Ising model in a very strong field at low temperatures produce non-Gibbsian measures. This shows that pathological behavior of renormalization-group transformations is even more widespread than previous examples already suggested.

AB - We show that decimation transformations applied to high-q Potts models result in non-Gibbsian measures even for temperatures higher than the transition temperature. We also show that majority transformations applied to the Ising model in a very strong field at low temperatures produce non-Gibbsian measures. This shows that pathological behavior of renormalization-group transformations is even more widespread than previous examples already suggested.

KW - NON-GIBBSIAN MEASURES

KW - REAL-SPACE RENORMALIZATION

KW - COMPLETE ANALYTICITY

KW - MAJORITY-RULE

KW - DECIMATION

KW - 1ST-ORDER PHASE-TRANSITIONS

KW - GROUP TRANSFORMATIONS

KW - LATTICE

M3 - Article

SN - 0022-4715

VL - 79

SP - 969

EP - 992

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 5-6

ER -

Pathological Behavior of Renormalization-Group Maps at High Fields and Above the Transition Temperature

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Keywords

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