As Dave Johnston said, no - unless you explicitly create a new Thread.
Of course, you can get new threads turning up if the method you call creates new threads as part of how it works.
There's a difference between threads and processes. Threads are Java's solution to multi-tasking (and a good solution it is too). A process is an operating system thing. Depending on your JVM, a new thread may or may not run in a new process.
Either way, all threads within a JVM access the same memory space. Slightly paranoid note: there are some synchronisation issues within JVM memory to do with CPU-level memory caches - see the documentation about the volatile keyword if you're doing serious multithreaded coding.
You can have multiple JVMs running with separate memory, e.g. if you run separate commands from the command line.