Summary
This paper contains a calculation, up to two loops, of the infra-red behaviour in three dimensions of the symmetric and massless Landau Hamiltonian withN components. For the critical exponent η, we get forN=0, 1, 2, 3, respectively, the results 0.047, 0.063, 0.076, 0.086. Due to the nonvalidity of hyperscaling, we cannot give at present the other standard critical exponents; for this we need to calculate as additional information the temperature dependence of the correlation length.
Riassunto
Questo lavoro contiene un calcolo, sino a due loops, dell'andamento infrarosso in tre dimensioni della hamiltoniana di Landau simmetrica e a massa nulla conN componenti. Per l'esponente critico η otteniamo perN=0, 1, 2, 3 i risultati 0.047, 0.063, 0.076, 0.086 rispettivamente. A causa della non validità dello hyperscaling, non possiamo presentemente dare gli altri esponenti critici standard; per questo dobbiamo calcolare come ulteriore informazione la dipendenza della lunghezza di correlazione dalla temperature.
Резюме
В этой статье, вплоть до двух петель, вычисляется инфракрасное поведение в трех измерениях симметричного и безмассового Гамильтониана Ландау сN компонентами. Для критической экспоненты η мы получаем дляN=0, 1, 2, 3 соответственно результаты: 0.047, 0.063, 0.076, 0.086. Из-за неприменимости гиперскейлинга мы не можем дать, в данный момент, других стандартных критических экспонент. Для этого необходима дополнительная информация о температурной зависимости корреляционной длины.
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Holwerda, M.J., van Neerven, W.L. & Van Royen, R.P. Critical phenomena in three dimensions for arbitraryN . Nuov Cim A 52, 53–76 (1979). https://doi.org/10.1007/BF02774940
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DOI: https://doi.org/10.1007/BF02774940