Interchain coupling, influence

Hooke s law relates stress (or strain) at a point to strain (or stress) at the same point and the structure of classical elasticity (see e.g. Love, Sokolnikoff) is built upon this linear relation. There are other relationships possible. One, as outlined above (see e.g. Green and Adkins) involves the large strain tensor Cjj which does not bear a simple relationship to the stress tensor, another involves the newer concepts of micropolar and micromorphic elasticity in which not only the stress but also the couple at a point must be related to the local variations of displacement and rotation. A third, which may prove to be very relevant to polymers, derives from non-local field theories in which not only the strain (or displacement) at a point but also that in the neighbourhood of the point needs to be taken into account. In polymers, where the chain is so much stiffer along its axis than any interchain stiffness (consequent upon the vastly different forces along and between chains) the displacement at any point is quite likely to be influenced by forces on chains some distance away. 

The problem of phase transitions is investigated in the Gorkov-Dzyalo-shinskii model of weakly coupled metallic chains using the multiplicative renormalization group method. It is found that while the type of the order that develops in the system is determined by the interchain interaction, the critical temperature is strongly influenced by the intrachain coupling. 

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