Both "Java Language Specification" and "Java Virtual Machine Specifications" are freely available. There are multiple JDK and virtual machine implementations, some open source and others commercial.
HotSpot is the most popular virtual machine, distributed with Oracle JDK. This is a commercial distribution and is pretty stable. However OpenJdk, initially developed by Sun Microsystems, is still the reference implementation, under GPL license.
There are many others implementations like JRockit, particularly designed for production environment, or J9 from IBM.
To find out which virtual machine is installed, type:
java -version
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