Publications 1990-1999

Publications are arranged in chronological order. Publications other than research articles, published in international journals, are encoded with a letter indicating the type of publication.

Key to types:

A – Published conference presentation
B – Books and contributions to books
C – Tutorial level articles, published in international refereed journals
D – Miscellaneous publications

1990

114. Guttmann, A.J. and Enting, I.G., On the area of square lattice polygons, J. Stat. Phys. 58, 475-84 (1990).

115. Guttmann, A.J. and Bursill, R., Critical exponent for the loop erased self-avoiding walk by Monte Carlo methods , J. Stat. Phys. 59, (1990) 1-9.

116. Guttmann, A.J. and Enting, I.G., The phase transition of the 3-dimensional 3-state Potts model, Nucl. Phys. B. (Conf. Suppl.) 17, (1990) 328-30. A

117. Guttmann, A.J. and Yang, S., Universal distance ratios for 2-d SAWs: Series Results, J. Phys. A: Math. Gen. 23, (1990) L117-9.

118. Brak, R., Guttmann, A.J. and Enting, I.G., Exact solution of the row-convex polygon perimeter generating function, J. Phys. A: Math. Gen. 23, (1990) 2319-26.

*119. Brak, R. and Guttmann, A.J., Exact solution of the staircase and row-convex polygon perimeter and area generating function, J. Phys. A: Math. Gen. 23, (1990) 4581-8.

120. Yang, S, Thompson C.J. and Guttmann, A.J., Density of hole states for the strongly correlated Hubbard model, Phys. Rev. B. 42, (1990) 8431-5.

121. Whittington, S.G. and Guttmann, A.J., Self-avoiding walks which cross a square, J. Phys. A: Math. Gen. 23, (1990) 5601-9.

*122. Brak, R. and Guttmann, A.J., Algebraic approximants: A new method of series analysis, J. Phys. A: Math. Gen. 23, (1990) L1331-7.

1991

123. Thompson, C.J., Yang, S., Guttmann, A.J. and Sykes, M.F., High temperature expansion for the strongly correlated Hubbard model in the limit of infinite dimension, J. Phys. A: Math. Gen. 24, (1991) 1261-80.

124. Guttmann, A.J. and Wang, J., The extension of self-avoiding random walk series in 2 dimensions, J. Phys. A: Math. Gen. 24, (1991) 3107-9.

125. Guttmann, A.J., Thompson, C.J. and Yang, S., Numerical Studies of the Hubbard Model, Nucl. Phys. B (Conf. Suppl.) 20, (1991) 694-8. A

126. Fisher, M.E., Guttmann, A.J. and Whittington, S.G., Two dimensional lattice vesicles and polygons, J. Phys. A: Math. Gen. 24, (1991) 3095-16.

127. Brak, R., Guttmann, A.J. and Whittington, S.G., On the behaviour of collapsing linear and branched polymers, J. of Mathematical Chemistry 8, (1991) 255-68.

128. Guttmann, A.J. and Yang, Y.S., The shortest path of SAWS with bridges, J. Phys. A: Math. Gen. 24, (1991) 1603-9.

1992

129. Guttmann, A.J., Planar polygons: Regular, Convex, Almost Convex, Staircase and Row Convex. In Proceedings of the 1991 Taipei Intl. Symposium on Statistical Mechanics, AIP Conference Proceedings 248, (1992) 12-43. A

130. Guttmann, A.J., Interacting Self-avoiding Walk and Polygon Systems: Models of Collapse. In Proceedings of the 1991 Taipei Intl. Symposium on Statistical Mechanics, AIP Conference Proceedings 248, (1992) 34-51. A

*131. Enting, I.G., Guttmann, A.J., Richmond, L.B. and Wormald, N.C., Enumeration of Almost Convex Polygons on the Square Lattice, Random Structures and Algorithms 3, 445-61.

132. Brak, R., Guttmann, A.J. and Whittington, S.G., A Collapse Transition in a Directed Walk Model, J. Phys. A: Math Gen. 25, (1992) 2437-46.

133. Enting, I.G.and Guttmann, A.J., Self-avoiding rings on the triangular lattice, J. Phys. A: Math Gen. 25, (1992) 2791-2807.

134. Yang, S., Thompson, C.J. and Guttmann, A.J., High-temperature expansions for the strongly correlated Falicov-Kimball model, Physica A. 184, (1992) 587-97.

1993

135. Guttmann, A.J. and Thompson, C.J., Subsonic potential flow and the transonic controversy, SIAM J. Appl. Math., 53, (1993) 48-59.

136. Prellberg, T., Owczarek. A.L., Brak, R. and Guttmann, A.J., Finite length scaling of collapsing directed walks, Phys. Rev. E., 48, (1993) 2386-96.

137. Guttmann, A.J. and Enting, I.G., Series studies of the Potts model. I: The simple cubic Ising model, J. Phys. A: Math. Gen., 26, (1993) 807-21.

*138. Conway, A., Enting, I.G. and Guttmann, A.J., Algebraic techniques for enumerating self-avoiding walks on the square lattice, J. Phys. A: Math. Gen., 26, (1993) 1519-34.

139. Conway, A., Brak, R. and Guttmann, A.J., Directed animals on two dimensional lattices, J. Phys. A: Math. Gen., 26, (1993) 3085-91.

140. Conway, A.and Guttmann, A.J., Enumeration of self avoiding trails on a square lattice using a transfer matrix technique, J. Phys. A: Math. Gen., 26, (1993) 1535-52.

*141. Guttmann, A.J. and Prellberg, T., Staircase polygons, elliptic integrals, Heun functions and lattice Green functions, Phys. Rev. E, 47, (1993) R2233-6.

142. Cardy, J.L. and Guttmann, A.J., Universal amplitude combinations for self-avoiding walks, polygons and trails, J. Phys. A: Math. Gen., 26, (1993) 2485-94.

143. Butera, P., Comi, M. and Guttmann, A.J., Critical exponents of the three-dimensional classical plane rotator model on the s.c. lattice from a high-temperature series analysis, Phys. Rev. E, 48, (1993) 13987-90.

144. Barton, N.G. and Guttmann, A.J., “The Mathematics-in-Industry Study Group: 1984-93 and Beyond”, Gazette of the Australian Mathematical Society, 20, (1993) 59-63. D

145. Guttmann, A.J., “The National Curriculum in Mathematics”. Principal Matters, 5, (1993) 11-12. D

146. Guttmann, A.J., “The National Statement and Profiles – What�s it all about?”, Viniculum, 30, (1993), 14-17. D

147. Guttmann, A.J. and Enting, I.G., Comment on “Low-Temperature Expansion for the Ising Model”, Phys. Rev. Lett., 70, (1993) 698.

148. Conway, A. and Guttmann, A.J., Lower bounds on the connective constant for square-lattice self-avoiding walks, J. Phys. A, 26, (1993) 3719-24.

149. Guttmann, A.J., Prellberg, T. and Owczarek, A.L., On the symmetry classes of planar self-avoiding walks, J. Phys. A, 26, (1993) 6615-23.

1994

150. Bennett-Wood, D., Brak, R., Guttmann, A.J., Owczarek, A.L. and Prellberg, T., Low temperature 2D polymer partition function scaling: series analysis results, J. Phys. A, 27, (1994) L1-8.

151. Briggs, K.M., Enting, I.G. and Guttmann, A.J., Series studies of the Potts model. II: bulk series for the square lattice, J. Phys. A: Math. Gen., 27, (1994) 1503-23.

152. Joyce, G.S. and Guttmann, A.J., The critical equation of state for mean-field theory and the generating function for directed, column-convex animals, J. Phys. A: Math. Gen., 27, (1994) 4359-67.

*153. Guttmann, A.J.and Enting, I.G., Series studies of the Potts model III: The 3-state model on the simple cubic lattice, J. Phys. A: Math. Gen., 27, (1994) 5801-12.

154. Glasser, M.L. and Guttmann, A.J., Lattice Green Function (at 0) for the 4d hypercubic lattice, J. Phys. A: Math. Gen., 27, (1994) 7011-14.

155. Conway, A.R. and Guttmann, A.J., Longitudinal size exponent for square lattice directed animals, J. Phys. A: Math. Gen., 27, (1994) 7007-10.

156. Enting, I.G., Guttmann, A.J. and Jensen, I., Low-temperature Series Expansions for the Spin-1 Ising Model, J. Phys. A: Math. Gen., 27, (1994) 6987-7005.

157. Guttmann, A.J. and Enting, I.G., The high-temperature specific heat exponent of the 3-d Ising model, J. Phys. A: Math. Gen., 27, (1994), 8007-8010.

*158. Owczarek, A.L., Prellberg, T., Bennett-Wood, D. and Guttmann, A.J., Universal distance ratios for interacting two-dimensional polymers, J. Phys. A: Math. Gen., 27, (1994), L919-925.

1995

159. Conway, A.R. and Guttmann, A.J., On two-dimensional percolation, J. Phys. A: Math. Gen., 28, (1995), 891-904.

160. Guttmann, A.J., Owczarek, A., Bennett-Wood, D. and Prellberg, T., Recent developments in the study of walks, polygons and the Ising model (Proc. XIIth Intl. Symposium on Lattice Field Theory) Nucl. Physics B (Suppl.), 42, (1995), 911-3. A.

*161. Essam, J.W. and Guttmann, A.J., Vicious walkers and directed polymer networks in general dimension, Phys. Rev. E, 52, (1995) 5849-62.

*162. Jensen, I. and Guttmann, A.J., Series expansions of the percolation probability for directed square and honeycomb lattices. J. Phys. A: Math. Gen., 28, (1995), 4813-33.

163. Bennett-Wood, D., Cardy, J.L., Flesia, S., Guttmann, A.J.,and Owczarek, A.L., Oriented self-avoiding walks with orientation dependent interactions, J. Phys. A: Math. Gen., 28, (1995), 5143-63.

164. Essam, J.W., and Guttmann, A.J., Directed compact percolation near a wall: II. Cluster length and size, J.Phys. A: Math. Gen., 28, (1995) 3591-3598.

165. Jensen, I., Guttmann, A.J. and Enting, I.G., The finite lattice method of series expansions (Proc. Computational Techniques and Application Conference CTAC 95), World Scientific (1995), 1-6. A.

1996

166. Jensen, I., and Guttmann, A.J., Series expansions of the percolation probability on the directed triangular lattice, J. Phys. A: Math. Gen., 29, (1996) 497-517.

167. Jensen, I. and Guttmann, A.J., Series expansions for two-dimensional directed percolation. (Proc. XIIIth Intl. Symposium on Lattice Field Theory), Nucl. Physics B (Suppl.), 47, (1996) 835-7. A.

168. Guttmann, A.J. and Enting, I.G., Inversion relations, the Ising model and self avoiding polygons, (Proc. XIIIth Intl. Symposium on Lattice Field Theory), Nucl. Physics B (Suppl.), 47, (1996) 735-8. A.

169. Essam, J.W. and Guttmann, A.J., Jensen, I., and TanlaKishani, D., Directed Percolation near a wall. J. Phys. A. : Math. Gen., 29, (1996), 1619-28.

170. Guttmann, A.J. and Enting, I.G., On the solvability of some statistical mechanical systems, Phys. Rev. Letters, 76, (1996), 344-7.

171. Kieu, T.C, McKellar B.H.J. and Guttmann, A.J., editors of Proc. XIIIth Intl. Symposium on Lattice Field Theory, Nucl. Physics B (Suppl.), 47, (1996). B.

172. Jensen, I., and Guttmann, A.J., Extrapolation procedure for low-temperature series for the square lattice spin-1 Ising model. J.Phys:Math. Gen., 29, (1996), 3817-36.

173. Jensen, I., Guttmann, A.J. and Enting, I.G., Low temperature expansions for the square Lattice Ising model with spin S>1. J. Phys. A: Math. Gen., 29, (1996), 3817-36.

174. Swierczak, E. and Guttmann, A.J., Self-avoiding walks and polygons on non-Euclidean lattices. J. Phys. A:Math. Gen., 29, (1996), 7485-500.

175. Conway, A.R. and Guttmann, A.J., Square lattice self-avoiding walks and corrections to scaling. Phys. Rev. Letts., 77, (1996), 5284-7.

1997

176. Guttmann, A.J., Inversion relations, the Ising model and polygons, Mathematical and Computer Modelling, 26, (1997), 315. A.

177. Conway, A.R., Guttmann, A.J., and Delest, M., On the number of three choice polygon, Mathematical and Computer Modelling, 26, (1997) 51-58.

178. Bousquet-Mélou, M. and Guttmann, A.J., Enumeration of three dimensional convex polygons, Annals of Combinatorics, 1, (1997), 27-53.

179. Bousquet-Mélou, M. and Guttmann, A.J., Three-dimensional self-avoiding convex polygons. Phys. Rev. E, 55, (1997), R6323-6.

180. Owczarek, A.L, Rechnitzer, A., Brak, R and Guttmann, A.J. On the hulls of directed percolation clusters. J. Phys. A., 30, (1997), 6679-91.

181. Jensen, I and Guttmann, A.J. and Enting, I.G., The Potts model on Kagomé and Honeycomb lattices, J. Phys. A., 30, (1997), 8067-8.

1998

182. Feldman, H., Guttmann, A.J., Jensen, I., Shrock, R. and Tsai, Shan-Ho, Studies of the Potts model on the honeycomb and triangular lattices: Low-temperature series and partition function zeros. J. Phys. A., 31, (1998), 2287-2310.

183. Bennett-Wood, D., Cardy, J.L., Enting, I.G., Guttmann, A.J. and Owczarek, A.L, On the non-universality of a critical exponent for self-avoiding walks. Nucl. Physics B, 528, (1998), 533-552.

184. Bennett-Wood, D., Enting, I.G., Gaunt, D.S., Guttmann, A.J. Leask, J.L. Owczarek, A.L. and Whittington, S.G., Exact enumeration study of free energies of interacting polygons and walks in two dimensions. J. Phys. A., 31, (1998), 4725-41.

185. Guttmann, A.J., Owczarek, A.L. and Viennot, X.G., Vicious walkers and Young Tableaux I: Without Walls, J. Phys. A., 31, (1998), 8123-35.

186. Jensen, I and Guttmann, A.J., Self-avoiding walks, neighbour-avoiding walks and trails on semi-regular lattices, J. Phys. A., 31, (1998), 8137-45.

1999

187. Guttmann A.J. and Conway, A.R., Hexagonal lattice directed site animals. Statistical Physics on the Eve of the 21st Century, eds. M.T. Batchelor and L.T. Wille pp. 491-504. Series in Advances in Statistical Mechanics, (World Scientific), (1999).

188. Jensen, I and Guttmann, A.J., Self-avoiding polygons on the square lattice, J. Phys. A., 31, (1999), 4867-76.

189. Bousquet-Mélou, M., Guttmann, A.J., Orrick, W.P. and Rechnitzer A, Inversion relations, resiprocity and polygons. Annals of Combinatorics, 3, (1999), 223-249.

190. Guttmann, A.J., (Guest Editor), Special issue of Annals of Combinatorics, vol. 3, Nos. 2-4, pp 115-484. On Statistical Mechanics and Combinatorics.