# Correlation lengths and scaling functions in the three-dimensional O(4) model

Engels J, Fromme L, Seniuch M (2003)

NUCLEAR PHYSICS B 675(3): 533-554.

*Journal Article*|

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*English*

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We investigate numerically the transverse and longitudinal correlation lengths of the three-dimensional O(4) model as a function of the external field H. From our data we calculate the scaling function of the transverse correlation length, and that of the longitudinal correlation length for T > T-C. We show that the scaling functions do not only describe the critical behaviours of the correlation lengths but encompass as well the predicted Goldstone effects, in particular the H-1/2_ dependence of the transverse correlation length for T < T-C. In addition, we determine the critical exponent delta = 4.824(9) and several critical amplitudes from which we derive the universal amplitude ratios R-x = 1.084(18), Q(C) = 0.431(9), Q(2)(T) = 4.91(8), Q(2)(L) = 1.265(24) and U-xi(C) = 1.99(1). The last result supports a relation between the longitudinal and transverse correlation functions, which was conjectured to hold below T-C but seems to be valid also at T-C. (C) 2003 Elsevier B.V. All rights reserved.

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Engels J, Fromme L, Seniuch M. Correlation lengths and scaling functions in the three-dimensional O(4) model.

*NUCLEAR PHYSICS B*. 2003;675(3):533-554.Engels, J., Fromme, L., & Seniuch, M. (2003). Correlation lengths and scaling functions in the three-dimensional O(4) model.

*NUCLEAR PHYSICS B*,*675*(3), 533-554.Engels, J., Fromme, L., and Seniuch, M. (2003). Correlation lengths and scaling functions in the three-dimensional O(4) model.

*NUCLEAR PHYSICS B*675, 533-554.Engels, J., Fromme, L., & Seniuch, M., 2003. Correlation lengths and scaling functions in the three-dimensional O(4) model.

*NUCLEAR PHYSICS B*, 675(3), p 533-554. J. Engels, L. Fromme, and M. Seniuch, “Correlation lengths and scaling functions in the three-dimensional O(4) model”,

*NUCLEAR PHYSICS B*, vol. 675, 2003, pp. 533-554. Engels, J., Fromme, L., Seniuch, M.: Correlation lengths and scaling functions in the three-dimensional O(4) model. NUCLEAR PHYSICS B. 675, 533-554 (2003).

Engels, Jürgen, Fromme, L, and Seniuch, M. “Correlation lengths and scaling functions in the three-dimensional O(4) model”.

*NUCLEAR PHYSICS B*675.3 (2003): 533-554.
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arXiv hep-lat/0307032

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