Computer Simulation Study of a Nematogenic LatticeGas Model with FourthRank Interactions
Abstract
We have considered a classical latticegas model, consisting of a threedimensional simplecubic lattice, whose sites host threecomponent unit vectors; pairs of nearestneighboring sites interact via the nematogenic potential <DF><TEX ID="S0217979202009986E001">\[ \Phi_{jk}= \epsilon \nu_j \nu_k P_4(\tau),\qquad \tau=\tau_{jk}= {\bf u}_j \cdot {\bf u}_k; \]</TEX></DF> here P_{4}(τ) denotes the fourth Legendre polynomial, nu_{j}=0,1 are occupation numbers, u _{j} are unit vectors (classical spins), and ∊ is a positive quantity setting the energy and temperature scales (i.e. T* =k_{B} T / ∊). The total Hamiltonian is given by <DF><TEX ID="S0217979202009986E002">\[ \Psi=\frac{W}{\epsilon}=\sum_{\{ j k \}} (\nu_j \nu_k) P_4({\bf u}_j \cdot {\bf u}_k) \mu N,\qquad N= \sum_k \nu_k, \] </TEX></DF> where ∑_{{j < k}} denotes sum over all distinct nearestneighboring pairs of lattice sites. The saturatedlattice version of this model defines a nematogenic lattice model, already studied in the literature, and found to possess a transition to an orientationally ordered phase at low temperature; moreover, according to available rigorous results, there exists a μ_{0}<0, such that, for all μ>μ_{0}, the system supports an ordering transition at a finite, μdependent, temperature. We present here a detailed study of the case μ=0, and characterize it by means of Monte Carlo simulation, Mean Field and Two Site Cluster treatments; the latter significantly improves the agreement with simulation results.
 Publication:

International Journal of Modern Physics B
 Pub Date:
 2002
 DOI:
 10.1142/S0217979202009986
 Bibcode:
 2002IJMPB..16.2901R
 Keywords:

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