Halliday & Matthiessen (1999: 407):
Thematic spaces in an ideational semantic network can be seen as a model of the systemic understanding of Theme and method of development articulated by Martin, where [Martin’s] “field” corresponds to what has been discussed here in terms of ideational semantic networks in the ideation base.
That is:
(1) Halliday & Matthiessen's thematic spaces in an ideational semantic network
is a systemic understanding of
Martin's Theme and method of development
(2) Halliday & Matthiessen's ideational semantics
corresponds to
Martin's field