Antiferromagnetism. The Kagomé Ising Net

Abstract

We can solve exactly the eigenvalue problem of the kagom Isingnetwith z = 4. The transition temperature lies a little below thanthatof the square lattice. Its value is determined by {e4Lc} = 3 +23and it teaches us that it is not determined only by thenumber ofnearest neighbors. In the case of antiferromagnetism,especially,the kagom lattice which does not fit toantiferromagnetic arrangementis disordered at all temperature andpossesses a finite zero pointentropy just as in the case of thetriangular lattice and the resultruns as follows: {(Sk(0))/R} = 1/(24{\textbar}pi2)q {\textbackslash}int02{\textbackslash}int0a log{ 21 - 4 (cos1 + cos2 + cos1 + 2) } d1 d2{\textbackslash}fallingdotseq 0.50183