We have performed a Monte Carlo study of dimensions for two dimensional linear chains of different lengths. These chains are composed of Gaussian units which interact through a 6-12 Lennard-Jones potential. From this study, the theta state for this model has been characterized. Scaling curves have been obtained and different universal exponents, such as the theta point exponent upsilon, upsilon(theta), and the cross-over exponent Phi(t) have been numerically evaluated. The results are compared with theoretical predictions and with the values corresponding to simulations in lattice models. The results for upsilon and upsilon(theta) agree with the theory, but our best estimation for the cross-over exponent is closer to the simple mean field estimation.