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E-International Scientific Research JournalISSN: 2094-1749 Volume: 2 Issue: 4, 2010which is the minimum of the standard FH free energy. Now, insert the decomposition (11) inthe total Hamiltonian, relations (1a) and (2), and expand it to second order around , togetWith the new bulk Hamiltonianwhich is quadratic in the field . The parameters and areExplicitly, we havewhere c and µ are those surface parameters defined in Eq. (10). The signs (+) and (-) are forhigh and low temperatures, respectively.The following step consists in the computation of the induced force away from thecritical point. To this end, use will be made of the new Hamiltonian, relations (12) and (13).322
E-International Scientific Research JournalISSN: 2094-1749 Volume: 2 Issue: 4, 2010Induced ForcesAs we said in the beginning, the critical fluctuations of the order parameter give rise to aninduced force, which is attractive and of long-range. The determination of the distance decayof such a force will be achieved through the knowledge of the pair-potential, denoted, .Here, r is the center-to-center distance of two interacting particles. Formally, and takingadvantage of the standard cumulant method [40,41], we show that the p-bodyinteractionenergy,, is directly proportional to the connected p-point correlation function,which is constructed with the field operatorNotice that for p = 1, the one-body potentialspatial translation symmetry. For p = 2, we get the pair-potentialis space-independent due to theExplicitly, we havewhereandare the connected two-point correlation functions of fields ψand, respectively. These functions are constructed with the Boltzmann323
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